{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T13:43:01Z","timestamp":1780321381328,"version":"3.54.1"},"reference-count":249,"publisher":"Emerald","issue":"3-4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017,8,8]]},"abstract":"<jats:p>Mathematical models are at the core of modern science and technology. An accurate description of behaviors, systems and processes often requires the use of complex models which are difficult to analyze and control. To facilitate analysis of and design for complex systems, model reduction theory and tools allow determining \u201csimpler\u201d models which preserve some of the features of the underlying complex description. A large variety of techniques, which can be distinguished depending on the features which are preserved in the reduction process, has been proposed to achieve this goal. One such a method is the moment matching approach.<\/jats:p>\n                  <jats:p>This monograph focuses on the problem of model reduction by moment matching for nonlinear systems. The central idea of the method is the preservation, for a prescribed class of inputs and under some technical assumptions, of the steady-state output response of the system to be reduced. We present the moment matching approach from this vantage point, covering the problems of model reduction for nonlinear systems, nonlinear time-delay systems, data-driven model reduction for nonlinear systems and model reduction for \u201cdiscontinuous\u201d input signals. Throughout the monograph linear systems, with their simple structure and strong properties, are used as a paradigm to facilitate understanding of the theory and provide foundation of the terminology and notation. The text is enriched by several numerical examples, physically motivated examples and with connections to well-established notions and tools, such as the phasor transform.<\/jats:p>","DOI":"10.1561\/2600000012","type":"journal-article","created":{"date-parts":[[2017,8,8]],"date-time":"2017-08-08T09:52:18Z","timestamp":1502185938000},"page":"224-409","source":"Crossref","is-referenced-by-count":61,"title":["Nonlinear Model Reduction by Moment Matching"],"prefix":"10.1108","volume":"4","author":[{"given":"Giordano","family":"Scarciotti","sequence":"first","affiliation":[{"name":"Imperial College London"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alessandro","family":"Astolfi","sequence":"additional","affiliation":[{"name":"Imperial College London and Universita di Roma \u201cTor Vergata\u201d"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"140","published-online":{"date-parts":[[2017,8,8]]},"reference":[{"key":"2026033114232718700_ref001","doi-asserted-by":"crossref","first-page":"3106","DOI":"10.23919\/ACC.1993.4793475","article-title":"Delayed positive feedback can stabilize oscillatory systems","volume-title":"Proceedings of the 1993 American Control Conference","author":"Abdallah","year":"1993"},{"issue":"5","key":"2026033114232718700_ref002","doi-asserted-by":"crossref","first-page":"693","DOI":"10.1109\/5.929650","article-title":"Simulation of high-speed interconnects","volume":"89","author":"Achar","year":"2001","journal-title":"Proceedings of the IEEE"},{"key":"2026033114232718700_ref003","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1070\/SM1971v015n01ABEH001531","article-title":"Analytic properties of Schmidt pairs for a Hankel operator and the generalized Schur-Takagi problem","volume":"15","author":"Adamjan","year":"1971","journal-title":"Mathematics of the USSR Sbornik"},{"issue":"1","key":"2026033114232718700_ref004","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/0167-6911(88)90037-0","article-title":"Comments on the stabilizability of the angular velocity of a rigid body","volume":"10","author":"Aeyels","year":"1988","journal-title":"Systems & Control Letters"},{"key":"2026033114232718700_ref005","first-page":"2491","article-title":"Approximation of time-delay systems","author":"Al-Amer","year":"2000"},{"issue":"10","key":"2026033114232718700_ref006","doi-asserted-by":"crossref","first-page":"1631","DOI":"10.1080\/00207729408949302","article-title":"New model reduction scheme for bilinear systems","volume":"25","author":"Al-Baiyat","year":"1994","journal-title":"International Journal of Systems Science"},{"issue":"3","key":"2026033114232718700_ref007","doi-asserted-by":"crossref","first-page":"709","DOI":"10.1080\/00207179108953642","article-title":"Model order reduction via real Schur-form decomposition","volume":"53","author":"Aldhaheri","year":"1991","journal-title":"International Journal of Control"},{"key":"2026033114232718700_ref008","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898718713","volume-title":"Approximation of Large-Scale Dynamical Systems","author":"Antoulas","year":"2005"},{"issue":"9","key":"2026033114232718700_ref009","first-page":"443\u2013448","article-title":"Polplatzierung bei der modellreduktion (on pole placement in model reduction)","volume":"55","author":"Antoulas","year":"2009","journal-title":"Automatisierungstechnik"},{"key":"2026033114232718700_ref010","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1016\/0024-3795(90)90141-X","article-title":"On the solution of the minimal rational interpolation problem","volume":"137-138","author":"Antoulas","year":"1990","journal-title":"Linear Algebra and Its Applications, Special Issue on Matrix Problems"},{"key":"2026033114232718700_ref011","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1090\/conm\/280\/04630","article-title":"A survey of model reduction methods for large-scale systems","volume":"280","author":"Antoulas","year":"2001","journal-title":"Contemporary Mathematics"},{"issue":"5","key":"2026033114232718700_ref012","doi-asserted-by":"crossref","first-page":"B889","DOI":"10.1137\/15M1041432","article-title":"Model reduction of bilinear systems in the Loewner framework","volume":"38","author":"Antoulas","year":"2016","journal-title":"SIAM Journal on Scientific Computing"},{"issue":"4","key":"2026033114232718700_ref013","doi-asserted-by":"crossref","first-page":"869","DOI":"10.1109\/TAC.1982.1103023","article-title":"Linear systems with delayed controls: A reduction","volume":"27","author":"Artstein","year":"1982","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"3","key":"2026033114232718700_ref014","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/S0167-6911(98)00089-9","article-title":"Output feedback stabilization of the angular velocity of a rigid body","volume":"36","author":"Astolfi","year":"1999","journal-title":"Systems & Control Letters"},{"key":"2026033114232718700_ref015","first-page":"4361","article-title":"A new look at model reduction by moment matching for linear systems","author":"Astolfi","year":"2007","journal-title":"In Proceedings of the 46th IEEE Conference on Decision and Control"},{"key":"2026033114232718700_ref016","first-page":"577","article-title":"Model reduction by moment matching","volume-title":"IFAC Proceedings Volumes","author":"Astolfi","year":"2007"},{"key":"2026033114232718700_ref017","first-page":"4873","article-title":"Model reduction by moment matching for nonlinear systems","author":"Astolfi","year":"2008","journal-title":"Proceedings of the 47th IEEE Conference on Decision and Control"},{"issue":"10","key":"2026033114232718700_ref018","doi-asserted-by":"crossref","first-page":"2321","DOI":"10.1109\/TAC.2010.2046044","article-title":"Model reduction by moment matching for linear and nonlinear systems","volume":"55","author":"Astolfi","year":"2010","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"10","key":"2026033114232718700_ref019","doi-asserted-by":"crossref","first-page":"2237","DOI":"10.1109\/TAC.2008.2006102","article-title":"Missing point estimation in models described by proper orthogonal decomposition","volume":"53","author":"Astrid","year":"2008","journal-title":"IEEE Transactions on Automatic Control"},{"key":"2026033114232718700_ref020","volume-title":"Adaptive Control","author":"\u00c5str\u00f6m","year":"1995"},{"issue":"1","key":"2026033114232718700_ref021","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/S0168-9274(02)00116-2","article-title":"Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems","volume":"43","author":"Bai","year":"2002","journal-title":"Applied Numerical Mathematics"},{"key":"2026033114232718700_ref022","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/S0024-3795(00)00291-3","article-title":"A partial Pad\u00e9-via-Lanczos method for reducedorder modeling","volume":"332","author":"Bai","year":"2001","journal-title":"Linear Algebra and its Applications"},{"issue":"2","key":"2026033114232718700_ref023","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1109\/43.743719","article-title":"Error bound for reduced system model by Pad\u00e9 approximation via the Lanczos process","volume":"18","author":"Bai","year":"1999","journal-title":"IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems"},{"key":"2026033114232718700_ref024","first-page":"2448","article-title":"Reinforcement learning in continuous time: advantage updating","volume":"4","author":"Baird","year":"1994"},{"key":"2026033114232718700_ref025","doi-asserted-by":"crossref","first-page":"496","DOI":"10.1016\/0022-0396(79)90033-0","article-title":"Spline approximations for functional differential equations","volume":"34","author":"Banks","year":"1979","journal-title":"Journal of Differential Equations"},{"issue":"256-270","key":"2026033114232718700_ref026","first-page":"27","article-title":"Cross-Gramian based model reduction for data-sparse systems","volume":"31","author":"Baur","year":"2008","journal-title":"Electronic Transactions on Numerical Analysis"},{"issue":"4","key":"2026033114232718700_ref027","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/s11831-014-9111-2","article-title":"Model order reduction for linear and nonlinear systems: a system-theoretic perspective","volume":"21","author":"Baur","year":"2014","journal-title":"Archives of Computational Methods in Engineering"},{"key":"2026033114232718700_ref028","doi-asserted-by":"crossref","DOI":"10.1109\/CDC.2008.4739158","article-title":"Interpolation theory for structure-preserving model reduction","author":"Beattie","year":"2008"},{"issue":"3","key":"2026033114232718700_ref029","doi-asserted-by":"crossref","first-page":"430","DOI":"10.1088\/0960-1317\/15\/3\/002","article-title":"Error indicators for fully automatic extraction of heat-transfer macromodels for MEMS","volume":"15","author":"Bechtold","year":"2004","journal-title":"Journal of Micromechanics and Microengineering"},{"key":"2026033114232718700_ref030","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/0025-5564(75)90028-0","article-title":"Time lags are not necessarily destabilizing","volume":"27","author":"Beddington","year":"1986","journal-title":"Math. Biosciences"},{"key":"2026033114232718700_ref031","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611972856","volume-title":"Nonlinear Control Under Nonconstant Delays","author":"Bekiaris-Liberis","year":"2013"},{"key":"2026033114232718700_ref032","volume-title":"Generalized Inverses: Theory and Applications","author":"Ben-Israel","year":"2003"},{"issue":"1","key":"2026033114232718700_ref033","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1109\/MCS.2004.1272745","article-title":"Solving large-scale control problems","volume":"24","author":"Benner","year":"2004","journal-title":"IEEE Control Systems"},{"issue":"2","key":"2026033114232718700_ref034","doi-asserted-by":"crossref","first-page":"B239","DOI":"10.1137\/14097255X","article-title":"Two-sided projection methods for nonlinear model order reduction","volume":"37","author":"Benner","year":"2015","journal-title":"SIAM Journal on Scientific Computing"},{"key":"2026033114232718700_ref035","first-page":"255","article-title":"Singular perturbation approximation of large, dense linear systems","author":"Benner","year":"2000","journal-title":"In Proceedings of the IEEE International Symposium on Computer-Aided Control System Design"},{"issue":"5","key":"2026033114232718700_ref036","first-page":"1123","article-title":"Efficient numerical algorithms for balanced stochastic truncation","volume":"11","author":"Benner","year":"2001","journal-title":"Applied Mathematics and Computer Science"},{"issue":"11","key":"2026033114232718700_ref037","doi-asserted-by":"crossref","first-page":"1701","DOI":"10.1016\/j.parco.2003.05.013","article-title":"State-space truncation methods for parallel model reduction of large-scale systems","volume":"29","author":"Benner","year":"2003","journal-title":"Parallel Computing"},{"key":"2026033114232718700_ref038","first-page":"3078","article-title":"Computing optimal Hankel norm approximations of large-scale systems","author":"Benner","year":"2004"},{"key":"2026033114232718700_ref039","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-62006-5","volume-title":"Stability Theory of Dynamical Systems","author":"Bhatia","year":"1970"},{"issue":"10","key":"2026033114232718700_ref040","doi-asserted-by":"crossref","first-page":"2624","DOI":"10.1016\/j.automatica.2014.08.023","article-title":"Adaptive dynamic programming and optimal control of nonlinear nonaffine systems","volume":"50","author":"Bian","year":"2014","journal-title":"Automatica"},{"key":"2026033114232718700_ref041","doi-asserted-by":"crossref","DOI":"10.1515\/9781400826155","volume-title":"Unsolved Problems in Mathematical Systems and Control Theory","author":"Blondel","year":"2004"},{"key":"2026033114232718700_ref042","volume-title":"An Introduction to Differentiable Manifolds and Riemannian Geometry","author":"Boothby","year":"2003","edition":"second edition"},{"key":"2026033114232718700_ref043","first-page":"610","article-title":"Analysis of drilling vibrations: a time-delay system approach","author":"Boussaada","year":"2012"},{"key":"2026033114232718700_ref044","volume-title":"Finite Dimensional Linear Systems","author":"Brockett","year":"1970"},{"issue":"5","key":"2026033114232718700_ref045","doi-asserted-by":"crossref","first-page":"1202","DOI":"10.1016\/j.cam.2008.12.029","article-title":"2-norm optimal model reduction for large scale discrete dynamical MIMO systems","volume":"233","author":"Bunse-Gerstner","year":"2010","journal-title":"Journal of Computational and Applied Mathematics"},{"issue":"1","key":"2026033114232718700_ref046","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/BF01744436","article-title":"A several complex variables approach to feedback stabilization of linear neutral delay-differential systems","volume":"17","author":"Byrnes","year":"1984","journal-title":"Mathematical Systems Theory"},{"key":"2026033114232718700_ref047","doi-asserted-by":"crossref","first-page":"1841","DOI":"10.1109\/9.471206","article-title":"A complete parameterization of all positive rational extensions of a covariance sequence","volume":"40","author":"Byrnes","year":"1995","journal-title":"IEEE Transactions on Automatic Control"},{"key":"2026033114232718700_ref048","doi-asserted-by":"crossref","first-page":"822","DOI":"10.1109\/9.928584","article-title":"A generalized entropy criterion for Nevanlinna-Pick interpolation with degree constraint","volume":"46","author":"Byrnes","year":"2001","journal-title":"IEEE Transactions on Automatic Control"},{"key":"2026033114232718700_ref049","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-5929-9","volume":"35","author":"Carr","year":"1981","journal-title":"Applications of Centre Manifold Theory"},{"key":"2026033114232718700_ref050","author":"Chen","year":"1999","journal-title":"Model order reduction for nonlinear systems"},{"issue":"2","key":"2026033114232718700_ref051","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1109\/43.370425","article-title":"Analysis of interconnect networks using complex frequency hopping (CFH)","volume":"14","author":"Chiprout","year":"1995","journal-title":"IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems"},{"issue":"6","key":"2026033114232718700_ref052","doi-asserted-by":"crossref","first-page":"792","DOI":"10.1093\/ietele\/e89-c.6.792","article-title":"MIMO interconnects order reductions by using the multiple point adaptive-order rational global Arnoldi algorithm","volume":"89","author":"Chu","year":"2006","journal-title":"IEICE Transactions on Electronics"},{"issue":"1","key":"2026033114232718700_ref053","doi-asserted-by":"crossref","first-page":"137","DOI":"10.2514\/2.4007","article-title":"On-line version of the eigensystem realization algorithm using data correlations","volume":"20","author":"Cooper","year":"1999","journal-title":"Journal of Guidance, Control, and Dynamics"},{"issue":"10","key":"2026033114232718700_ref054","doi-asserted-by":"crossref","first-page":"1604","DOI":"10.1016\/j.automatica.2010.06.030","article-title":"A comparison between LQR control for a long string of SISO systems and LQR control of the infinite spatially invariant version","volume":"46","author":"Curtain","year":"2010","journal-title":"Automatica"},{"issue":"7","key":"2026033114232718700_ref055","doi-asserted-by":"crossref","first-page":"964","DOI":"10.1109\/9.701100","article-title":"A paradigm of ill-posedness with respect to time delays","volume":"43","author":"Datko","year":"1998","journal-title":"IEEE Transactions on Automatic Control"},{"key":"2026033114232718700_ref056","author":"Davis","year":"1998"},{"key":"2026033114232718700_ref057","author":"Doyle","year":"1992"},{"issue":"8","key":"2026033114232718700_ref058","doi-asserted-by":"crossref","first-page":"546","DOI":"10.1016\/j.sysconle.2011.04.013","article-title":"Adaptive rational Krylov subspaces for largescale dynamical systems","volume":"60","author":"Druskin","year":"2011","journal-title":"Systems & Control Letters"},{"key":"2026033114232718700_ref059","first-page":"127","article-title":"Model reduction with balanced realizations: An error bound and a frequency weighted generalization","author":"Enns","year":"1984"},{"issue":"5","key":"2026033114232718700_ref060","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1109\/43.384428","article-title":"Efficient linear circuit analysis by Pade approximation via the Lanczos process","volume":"14","author":"Feldmann","year":"1995","journal-title":"IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems"},{"issue":"2","key":"2026033114232718700_ref061","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1109\/TAC.1983.1103195","article-title":"On the structure of balanced and other principal representations of SISO systems","volume":"28","author":"Fernando","year":"1983","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"5","key":"2026033114232718700_ref062","doi-asserted-by":"crossref","first-page":"504","DOI":"10.1109\/TCS.1984.1085524","article-title":"On a fundamental property of the crossGramian matrix","volume":"31","author":"Fernando","year":"1984","journal-title":"IEEE Transactions on Circuits and Systems"},{"issue":"7","key":"2026033114232718700_ref063","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1016\/j.sysconle.2013.03.006","article-title":"Interpolatory","volume":"62","author":"Flagg","year":"2013","journal-title":"\u221e model reduction. Systems & Control Letters"},{"key":"2026033114232718700_ref064","author":"Fortuna","year":"1992"},{"key":"2026033114232718700_ref065","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1017\/S0962492902000120","article-title":"Model reduction methods based on Krylov subspaces","volume":"12","author":"Freund","year":"2003","journal-title":"Acta Numerica"},{"key":"2026033114232718700_ref066","first-page":"80","article-title":"SPRIM: structure-preserving reduced-order interconnect macromodeling","author":"Freund","year":"2004","journal-title":"In IEEE\/ACM International Conference on Computer Aided Design"},{"issue":"3","key":"2026033114232718700_ref067","doi-asserted-by":"crossref","first-page":"694","DOI":"10.1299\/jsdd.2.694","article-title":"Balanced realization and model order reduction for portHamiltonian systems","volume":"2","author":"Fujimoto","year":"2008","journal-title":"Journal of System Design and Dynamics"},{"issue":"1","key":"2026033114232718700_ref068","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1109\/TAC.2004.840476","article-title":"Nonlinear input-normal realizations based on the differential eigenstructure of Hankel operators","volume":"50","author":"Fujimoto","year":"2005","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"7","key":"2026033114232718700_ref069","doi-asserted-by":"crossref","first-page":"4591","DOI":"10.1137\/070695332","article-title":"Balanced realization and model order reduction for nonlinear systems based on singular value analysis","volume":"48","author":"Fujimoto","year":"2010","journal-title":"SIAM Journal on Control and Optimization"},{"issue":"4","key":"2026033114232718700_ref070","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1016\/j.sysconle.2007.08.015","article-title":"Computation of nonlinear balanced realization and model reduction based on Taylor series expansion","volume":"57","author":"Fujimoto","year":"2008","journal-title":"Systems & Control Letters"},{"issue":"5","key":"2026033114232718700_ref071","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/0893-9659(94)90077-9","article-title":"Asymptotic waveform evaluation via a Lanczos method","volume":"7","author":"Gallivan","year":"1994","journal-title":"Applied Mathematics Letters"},{"issue":"1","key":"2026033114232718700_ref072","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/j.cam.2003.08.026","article-title":"Sylvester equations and projection-based model reduction","volume":"162","author":"Gallivan","year":"2004","journal-title":"Journal of Computational and Applied Mathematics"},{"issue":"2","key":"2026033114232718700_ref073","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1137\/S0895479803423925","article-title":"Model reduction of MIMO systems via tangential interpolation","volume":"26","author":"Gallivan","year":"2004","journal-title":"SIAM Journal on Matrix Analysis and Applications"},{"key":"2026033114232718700_ref074","article-title":"Model reduction and the solution of Sylvester equations","author":"Gallivan","year":"2006"},{"issue":"2","key":"2026033114232718700_ref075","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1080\/00207729008910366","article-title":"Model reduction in limited time and frequency intervals","volume":"21","author":"Gawronski","year":"1990","journal-title":"International Journal of Systems Science"},{"key":"2026033114232718700_ref076","volume-title":"Partial Realization of Covariance Sequences","author":"Georgiou","year":"1983"},{"key":"2026033114232718700_ref077","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1109\/9.751366","article-title":"The interpolation problem with a degree constraint","volume":"44","author":"Georgiou","year":"1999","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"2","key":"2026033114232718700_ref078","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1080\/00207179108953623","article-title":"Approximation of delay systems \u2013 a case study","volume":"53","author":"Glader","year":"1991","journal-title":"International Journal of Control"},{"issue":"6","key":"2026033114232718700_ref079","doi-asserted-by":"crossref","first-page":"1115","DOI":"10.1080\/00207178408933239","article-title":"All optimal Hankel-norm approximations of linear multivariable systems and their L\u221e-error bounds","volume":"39","author":"Glover","year":"1984","journal-title":"International Journal of Control"},{"key":"2026033114232718700_ref080","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/BF02551374","article-title":"Rational approximation of a class of infinite dimensional system I: Singular value of Hankel operator","volume":"3","author":"Glover","year":"1990","journal-title":"Mathematics of Control, Signals and Systems"},{"key":"2026033114232718700_ref081","first-page":"278","article-title":"An extension of stability criteria for linear and nonlinear time delay systems","author":"Goubet","year":"1995"},{"key":"2026033114232718700_ref082","first-page":"2862","article-title":"General input balancing and model reduction for linear and nonlinear systems","author":"Gray","year":"1997"},{"key":"2026033114232718700_ref083","first-page":"3582","article-title":"Nonlinear Hilbert adjoints: properties and applications to Hankel singular value analysis","author":"Gray","year":"2001"},{"issue":"4","key":"2026033114232718700_ref084","doi-asserted-by":"crossref","first-page":"653","DOI":"10.1016\/j.automatica.2005.12.007","article-title":"Balanced realizations near stable invariant manifolds","volume":"42","author":"Gray","year":"2006","journal-title":"Automatica"},{"issue":"3","key":"2026033114232718700_ref085","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1051\/m2an:2007031","article-title":"Efficient reducedbasis treatment of nonaffine and nonlinear partial differential equations","volume":"41","author":"Grepl","year":"2007","journal-title":"ESAIM: Mathematical Modelling and Numerical Analysis"},{"key":"2026033114232718700_ref086","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1137\/1002004","article-title":"Some applications of the pseudoinverse of a matrix","author":"Greville","year":"1960","journal-title":"SIAM Rev. 2"},{"key":"2026033114232718700_ref087","author":"Grimme","year":"1997","journal-title":"Krylov projection methods for model reduction"},{"key":"2026033114232718700_ref088","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02141739","article-title":"Model reduction of state space systems via an implicitly restarted Lanczos method","volume":"12","author":"Grimme","year":"1995","journal-title":"Numer. Algorithms"},{"key":"2026033114232718700_ref089","first-page":"389","article-title":"QLMOR: A new projection-based approach for nonlinear model order reduction","author":"Gu","year":"2009"},{"issue":"9","key":"2026033114232718700_ref090","doi-asserted-by":"crossref","first-page":"1307","DOI":"10.1109\/TCAD.2011.2142184","article-title":"QLMOR: A projection-based nonlinear model order reduction approach using quadratic-linear representation of nonlinear systems","volume":"30","author":"Gu","year":"2011","journal-title":"IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems"},{"issue":"6","key":"2026033114232718700_ref091","doi-asserted-by":"crossref","DOI":"10.1109\/9.24229","article-title":"Approximation of infinitedimensional systems","volume":"34","author":"Gu","year":"1992","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"8","key":"2026033114232718700_ref092","doi-asserted-by":"crossref","first-page":"748","DOI":"10.1080\/00207170410001713448","article-title":"A survey of model reduction by balanced truncation and some new results","volume":"77","author":"Gugercin","year":"2004","journal-title":"International Journal of Control"},{"key":"2026033114232718700_ref093","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1007\/3-540-27909-1_2","volume-title":"Dimension reduction of large-scale systems","author":"Gugercin","year":"2005"},{"issue":"1","key":"2026033114232718700_ref094","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/j.automatica.2007.05.007","article-title":"Krylov projection framework for Fourier model reduction","volume":"44","author":"Gugercin","year":"2008","journal-title":"Automatica"},{"issue":"2","key":"2026033114232718700_ref095","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1137\/060666123","article-title":"2 model reduction for largescale linear dynamical systems","volume":"30","author":"Gugercin","year":"2008","journal-title":"SIAM Journal on Matrix Analysis and Applications"},{"issue":"9","key":"2026033114232718700_ref096","doi-asserted-by":"crossref","first-page":"1963","DOI":"10.1016\/j.automatica.2012.05.052","article-title":"Structurepreserving tangential interpolation for model reduction of port-Hamiltonian systems","volume":"48","author":"Gugercin","year":"2012","journal-title":"Automatica"},{"key":"2026033114232718700_ref097","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1016\/0022-0396(74)90080-1","article-title":"Behavior near constant solutions of functional differential equations","volume":"15","author":"Hale","year":"1974","journal-title":"Journal of differential equations"},{"key":"2026033114232718700_ref098","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-9892-2","volume-title":"Theory of Functional Differential Equations","author":"Hale","year":"1977"},{"key":"2026033114232718700_ref099","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4342-7","volume-title":"Introduction to Functional Differential Equations","author":"Hale","year":"1993"},{"key":"2026033114232718700_ref100","first-page":"275","article-title":"Effects of small delays on stability and control","volume":"122","author":"Hale","year":"2001","journal-title":"Operator Theory: Advances and Applications"},{"issue":"1-2","key":"2026033114232718700_ref101","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1093\/imamci\/19.1_and_2.5","article-title":"Strong stabilization of neutral functional differential equations","volume":"19","author":"Hale","year":"2002","journal-title":"IMA Journal of Mathematical Control and Information"},{"key":"2026033114232718700_ref102","doi-asserted-by":"crossref","DOI":"10.1007\/b100032","volume-title":"Dynamics in Infinite Dimensions","author":"Hale","year":"2002"},{"key":"2026033114232718700_ref103","doi-asserted-by":"crossref","first-page":"733","DOI":"10.1080\/00207179608921653","article-title":"Reduced-order models with delay","volume":"64","author":"Halevi","year":"1996","journal-title":"International Journal of Control"},{"issue":"11","key":"2026033114232718700_ref104","doi-asserted-by":"crossref","first-page":"111701","DOI":"10.1063\/1.4901016","article-title":"Dynamic mode decomposition for large and streaming datasets","volume":"26","author":"Hemati","year":"2014","journal-title":"Physics of Fluids"},{"key":"2026033114232718700_ref105","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1007\/3-540-27909-1_10","volume-title":"Dimension Reduction of Large-Scale Systems","author":"Hinze","year":"2005"},{"issue":"4","key":"2026033114232718700_ref106","doi-asserted-by":"crossref","first-page":"934","DOI":"10.1109\/TCST.2011.2157694","article-title":"Recursive predictorbased subspace identification with application to the real-time closed-loop tracking of flutter","volume":"20","author":"Houtzager","year":"2012","journal-title":"IEEE Transactions on Control Systems Technology"},{"key":"2026033114232718700_ref107","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898718683","volume-title":"Nonlinear Output Regulation: Theory and Applications","author":"Huang","year":"2004"},{"key":"2026033114232718700_ref108","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1080\/002071799221415","article-title":"Automatic vehicle following with integrated throttle and brake control","volume":"72","author":"Huang","year":"1999","journal-title":"International Journal of Control"},{"issue":"12","key":"2026033114232718700_ref109","doi-asserted-by":"crossref","first-page":"3098","DOI":"10.1016\/j.automatica.2012.08.021","article-title":"Block circulant and block Toeplitz approximants of a class of spatially distributed systems\u2013An LQR perspective","volume":"48","author":"Iftime","year":"2012","journal-title":"Automatica"},{"key":"2026033114232718700_ref110","doi-asserted-by":"crossref","first-page":"657","DOI":"10.1109\/25.260745","article-title":"Autonomous intelligent cruise control","volume":"42","author":"Ioannou","year":"1993","journal-title":"IEEE Transactions on Vehicular Technology"},{"key":"2026033114232718700_ref111","first-page":"5518","article-title":"Families of reduced order models that achieve nonlinear moment matching","author":"Ionescu","year":"2013"},{"issue":"10","key":"2026033114232718700_ref112","doi-asserted-by":"crossref","first-page":"2837","DOI":"10.1109\/TAC.2015.2502187","article-title":"Nonlinear moment matching-based model order reduction","volume":"61","author":"Ionescu","year":"2016","journal-title":"IEEE Transactions on Automatic Control"},{"key":"2026033114232718700_ref113","first-page":"1412","article-title":"Moment matching with prescribed poles and zeros for infinite-dimensional systems","author":"Ionescu","year":"2012"},{"key":"2026033114232718700_ref114","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/j.sysconle.2013.10.011","article-title":"Families of moment matching based, low order approximations for linear systems","volume":"64","author":"Ionescu","year":"2014","journal-title":"Systems & Control Letters"},{"key":"2026033114232718700_ref115","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-84628-615-5","volume-title":"Nonlinear Control Systems","author":"Isidori","year":"1995","edition":"Third edition"},{"issue":"1","key":"2026033114232718700_ref116","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.arcontrol.2008.01.001","article-title":"Steady-state behaviors in nonlinear systems with an application to robust disturbance rejection","volume":"32","author":"Isidori","year":"2008","journal-title":"Annual Reviews in Control"},{"issue":"3","key":"2026033114232718700_ref117","doi-asserted-by":"crossref","first-page":"633","DOI":"10.1137\/S0895479895279873","article-title":"Implicitly restarted Krylov subspace methods for stable partial realizations","volume":"18","author":"Jaimoukha","year":"1997","journal-title":"SIAM Journal on Matrix Analysis and Applications"},{"issue":"10","key":"2026033114232718700_ref118","doi-asserted-by":"crossref","first-page":"2699","DOI":"10.1016\/j.automatica.2012.06.096","article-title":"Computational adaptive optimal control for continuous-time linear systems with completely unknown dynamics","volume":"48","author":"Jiang","year":"2012","journal-title":"Automatica"},{"issue":"5","key":"2026033114232718700_ref119","doi-asserted-by":"crossref","first-page":"882","DOI":"10.1109\/TNNLS.2013.2294968","article-title":"Robust adaptive dynamic programming and feedback stabilization of nonlinear systems","volume":"25","author":"Jiang","year":"2014","journal-title":"IEEE Transactions on Neural Networks and Learning Systems"},{"key":"2026033114232718700_ref120","author":"Kalman","year":"1969","journal-title":"Topics in Mathematical System Theory"},{"issue":"2","key":"2026033114232718700_ref121","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/0167-6911(93)90021-W","article-title":"Characterization of the solution to the optimal H\u221e model reduction problem","volume":"20","author":"Kavrano\u011flu","year":"1993","journal-title":"Systems & Control Letters"},{"key":"2026033114232718700_ref122","volume-title":"Nonlinear Systems","author":"Khalil","year":"2001","edition":"third edition"},{"key":"2026033114232718700_ref123","first-page":"1","article-title":"Robust stability analysis of time delay systems: A survey","author":"Kharitonov","year":"1998"},{"key":"2026033114232718700_ref124","author":"Kimura"},{"key":"2026033114232718700_ref125","first-page":"499","article-title":"Positive partial realization of covariance sequences","author":"Kimura","year":"1986","journal-title":"Modeling, Identification and Robust Control"},{"key":"2026033114232718700_ref126","author":"Kolmanovskii","year":"1986","journal-title":"Stability of Functional Differential Equations"},{"key":"2026033114232718700_ref127","first-page":"1993","article-title":"Delay effects on stability: A survey","author":"Kolmanovskii","year":"1999"},{"issue":"2","key":"2026033114232718700_ref128","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1109\/TMAG.2013.2285442","article-title":"A posteriori error bounds for Krylov-based fast frequency sweeps of finiteelement systems","volume":"50","author":"Konkel","year":"2014","journal-title":"IEEE Transactions on Magnetics"},{"key":"2026033114232718700_ref129","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1007\/978-1-4757-2204-8_21","volume-title":"Systems, Models and Feedback: Theory and Applications","author":"Krener","year":"1992"},{"issue":"2","key":"2026033114232718700_ref131","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1023\/A:1021732508059","article-title":"Control of the Burgers equation by a reducedorder approach using proper orthogonal decomposition","volume":"102","author":"Kunisch","year":"1999","journal-title":"Journal of Optimization Theory and Applications"},{"issue":"01","key":"2026033114232718700_ref132","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1051\/m2an:2007054","article-title":"Proper orthogonal decomposition for optimality systems","volume":"42","author":"Kunisch","year":"2008","journal-title":"ESAIM: Mathematical Modelling and Numerical Analysis"},{"issue":"6","key":"2026033114232718700_ref133","doi-asserted-by":"crossref","first-page":"946","DOI":"10.1109\/TAC.2003.812779","article-title":"Error bounds for balanced model reduction of linear time-varying systems","volume":"48","author":"Lall","year":"2003","journal-title":"IEEE Transactions on Automatic Control"},{"key":"2026033114232718700_ref134","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1002\/rnc.657","article-title":"A subspace approach to balanced truncation for model reduction of nonlinear control systems","volume":"12","author":"Lall","year":"2002","journal-title":"International Journal on Robust and Nonlinear Control"},{"key":"2026033114232718700_ref135","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1016\/S0167-2789(03)00227-6","article-title":"Structure-preserving model reduction for mechanical systems","volume":"184","author":"Lall","year":"2003","journal-title":"Physica D"},{"issue":"2","key":"2026033114232718700_ref136","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1109\/TAC.1987.1104549","article-title":"Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms","volume":"32","author":"Laub","year":"1987","journal-title":"IEEE Transactions on Automatic Control"},{"key":"2026033114232718700_ref137","first-page":"296","article-title":"Powers of tensors and fast matrix multiplication","author":"Le Gall","year":"2014"},{"key":"2026033114232718700_ref138","first-page":"1151","article-title":"Reduction of large circuit models via low rank approximate gramians","volume":"11","author":"Li","year":"2001","journal-title":"International Journal of Applied Mathematics and Computer Science"},{"issue":"2","key":"2026033114232718700_ref139","doi-asserted-by":"crossref","first-page":"179","DOI":"10.4310\/CMS.2005.v3.n2.a6","article-title":"Structure-preserving model reduction using a Krylov subspace projection formulation","volume":"3","author":"Li","year":"2005","journal-title":"Communications in Mathematical Sciences"},{"issue":"2","key":"2026033114232718700_ref140","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1080\/00207178608933615","article-title":"Controller reduction via stable factorization and balancing","volume":"44","author":"Liu","year":"1986","journal-title":"International Journal of Control"},{"key":"2026033114232718700_ref141","author":"Lorenz","year":"1956"},{"key":"2026033114232718700_ref142","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/0025-5564(86)90133-1","article-title":"Two delays may not destabilize although either delay can","volume":"82","author":"MacDonald","year":"1986","journal-title":"Math Biosciences"},{"issue":"3","key":"2026033114232718700_ref143","doi-asserted-by":"crossref","first-page":"887","DOI":"10.2514\/1.45768","article-title":"Observer\/Kalman-filter timevarying system identification","volume":"33","author":"Majji","year":"2010","journal-title":"Journal of Guidance, Control, and Dynamics"},{"key":"2026033114232718700_ref144","doi-asserted-by":"crossref","first-page":"932","DOI":"10.1080\/002071799220678","article-title":"Laguerre and Kautz shift approximations of delay systems","volume":"72","author":"M\u00e4kil\u00e4","year":"1999","journal-title":"International Journal of Control"},{"issue":"6","key":"2026033114232718700_ref145","doi-asserted-by":"crossref","first-page":"1897","DOI":"10.1137\/S0363012998339678","article-title":"Shift operator induced approximations of delay systems","volume":"37","author":"M\u00e4kil\u00e4","year":"1999","journal-title":"SIAM Journal of Control and Optimization"},{"issue":"2-3","key":"2026033114232718700_ref146","doi-asserted-by":"crossref","first-page":"634","DOI":"10.1016\/j.laa.2007.03.008","article-title":"A framework for the solution of the generalized realization problem","volume":"425","author":"Mayo","year":"2007","journal-title":"Linear Algebra and its Applications"},{"issue":"12","key":"2026033114232718700_ref147","doi-asserted-by":"crossref","first-page":"1341","DOI":"10.1109\/9.61011","article-title":"Fractional balanced reduction: model reduction via a fractional representation","volume":"35","author":"Meyer","year":"1990","journal-title":"IEEE Transactions on Automatic Control"},{"key":"2026033114232718700_ref148","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898718645","volume-title":"Stability and Stabilization of Time-Delay Systems: An Eigenvalue-Based Approach","author":"Michiels","year":"2007"},{"issue":"7","key":"2026033114232718700_ref149","doi-asserted-by":"crossref","first-page":"1519","DOI":"10.1109\/TAC.2010.2042318","article-title":"String instability in classes of linear time invariant formation control with limited communication range","volume":"55","author":"Middleton","year":"2010","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"1","key":"2026033114232718700_ref150","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1109\/TAC.1981.1102568","article-title":"Principal component analysis in linear systems: controllability, observability, and model reduction","volume":"26","author":"Moore","year":"1981","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"9","key":"2026033114232718700_ref151","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1109\/TCS.1976.1084254","article-title":"Synthesis of minimum roundoff noise fixed point digital filters","volume":"23","author":"Mullis","year":"1976","journal-title":"IEEE Transactions on Circuits and Systems"},{"issue":"1-2","key":"2026033114232718700_ref152","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1016\/j.jsv.2007.06.037","article-title":"Avoiding harmful oscillations in a drillstring through dynamical analysis","volume":"307","author":"Navarro-L\u00f3pez","year":"2007","journal-title":"Journal of Sound and Vibration"},{"key":"2026033114232718700_ref153","volume-title":"Delay Effects on Stability","author":"Niculescu","year":"2001"},{"key":"2026033114232718700_ref154","first-page":"1495","article-title":"Delay-dependent stability of linear systems with delayed state: an LMI approach","author":"Niculescu","year":"1995"},{"key":"2026033114232718700_ref155","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2101-0","volume-title":"Nonlinear Dynamical Control Systems","author":"Nijmeijer","year":"1990"},{"key":"2026033114232718700_ref156","volume-title":"Electric Circuits","author":"Nilsson","year":"2008","edition":"tenth edition"},{"key":"2026033114232718700_ref157","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1017\/S0022112003006694","article-title":"A hierarchy of low-dimensional models for the transient and post-transient cylinder wake","volume":"497","author":"Noack","year":"2003","journal-title":"Journal of Fluid Mechanics"},{"issue":"8","key":"2026033114232718700_ref158","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1109\/43.712097","article-title":"PRIMA: passive reduced-order interconnect macromodeling algorithm","volume":"17","author":"Odabasioglu","year":"1998","journal-title":"IEEE Transactions on ComputerAided Design of Integrated Circuits and Systems"},{"key":"2026033114232718700_ref159","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/S0005-1098(98)00158-7","article-title":"Formulas for Hankel singular values and vectors for a class of input delay systems","volume":"35","author":"Ohta","year":"1999","journal-title":"Automatica"},{"key":"2026033114232718700_ref160","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1109\/TAC.1984.1103536","article-title":"A sufficiently large time delay in feedback loop must destroy exponential stability of any decay rate","volume":"29","author":"Olbrot","year":"1984","journal-title":"IEEE Transactions on Automatic Control"},{"key":"2026033114232718700_ref161","first-page":"838","article-title":"A geometric characterisation of persistently exciting signals generated by autonomous systems","author":"Padoan","year":"2016"},{"key":"2026033114232718700_ref162","first-page":"3843","article-title":"A geometric characterisation of the persistence of excitation condition for signals generated by discretetime autonomous systems","author":"Padoan","year":"2016"},{"key":"2026033114232718700_ref163","doi-asserted-by":"crossref","DOI":"10.1109\/TAC.2017.2687760","article-title":"A geometric characterisation of the persistence of excitation condition for the solutions of autonomous systems","author":"Padoan","year":"2017","journal-title":"To appear on IEEE Transactions on Automatic Control"},{"key":"2026033114232718700_ref164","first-page":"5512","article-title":"A greedy rational Krylov method for 2-pseudooptimal model order reduction with preservation of stability","author":"Panzer","year":"2013"},{"key":"2026033114232718700_ref165","doi-asserted-by":"crossref","first-page":"4484","DOI":"10.23919\/ECC.2013.6669657","article-title":"2 and \u221e error bounds for model order reduction of second order systems by Krylov subspace methods","author":"Panzer","year":"2013","journal-title":"Proceedings of the 2013 European Control Conference"},{"issue":"2","key":"2026033114232718700_ref166","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1162\/neco.1991.3.2.246","article-title":"Universal approximation using radial-basisfunction networks","volume":"3","author":"Park","year":"1991","journal-title":"Neural Computation"},{"key":"2026033114232718700_ref167","doi-asserted-by":"crossref","DOI":"10.1007\/0-8176-4465-2","volume-title":"Uniform Output Regulation of Nonlinear Systems: A Convergent Dynamics Approach","author":"Pavlov","year":"2006"},{"issue":"2-3","key":"2026033114232718700_ref168","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1016\/j.laa.2006.01.007","article-title":"Algorithms for model reduction of large dynamical systems","volume":"415","author":"Penzl","year":"2006","journal-title":"Linear Algebra and its Applications"},{"issue":"2","key":"2026033114232718700_ref169","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1109\/TAC.1982.1102945","article-title":"Model reduction via balanced state space representations","volume":"27","author":"Pernebo","year":"1982","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"8","key":"2026033114232718700_ref170","doi-asserted-by":"crossref","first-page":"1027","DOI":"10.1109\/TCAD.2003.814949","article-title":"Guaranteed passive balancing transformations for model order reduction","volume":"22","author":"Phillips","year":"2003","journal-title":"IEEE Transactions on ComputerAided Design of Integrated Circuits and Systems"},{"key":"2026033114232718700_ref171","first-page":"184","article-title":"Projection frameworks for model reduction of weakly nonlinear systems","author":"Phillips","year":"2000"},{"issue":"2","key":"2026033114232718700_ref172","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1109\/TCAD.2002.806605","article-title":"Projection-based approaches for model reduction of weakly nonlinear, time-varying systems","volume":"22","author":"Phillips","year":"2003","journal-title":"IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems"},{"issue":"1","key":"2026033114232718700_ref173","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1109\/TCAD.2004.839472","article-title":"Poor man\u2019s TBR: a simple model reduction scheme","volume":"24","author":"Phillips","year":"2005","journal-title":"IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems"},{"issue":"4","key":"2026033114232718700_ref174","doi-asserted-by":"crossref","first-page":"352","DOI":"10.1109\/43.45867","article-title":"Asymptotic waveform evaluation for timing analysis","volume":"9","author":"Pillage","year":"1990","journal-title":"IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems"},{"issue":"4","key":"2026033114232718700_ref175","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1016\/j.automatica.2010.01.018","article-title":"Structure preserving model reduction of port-Hamiltonian systems by moment matching at infinity","volume":"46","author":"Polyuga","year":"2010","journal-title":"Automatica"},{"issue":"6","key":"2026033114232718700_ref176","doi-asserted-by":"crossref","first-page":"1458","DOI":"10.1109\/TAC.2011.2128650","article-title":"Structure preserving moment matching for port-Hamiltonian systems: Arnoldi and Lanczos","volume":"56","author":"Polyuga","year":"2011","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"3","key":"2026033114232718700_ref177","doi-asserted-by":"crossref","first-page":"412","DOI":"10.1016\/j.sysconle.2011.12.008","article-title":"Effortand flow-constraint reduction methods for structure preserving model reduction of port-Hamiltonian systems","volume":"61","author":"Polyuga","year":"2012","journal-title":"Systems & Control Letters"},{"key":"2026033114232718700_ref178","first-page":"237","article-title":"Model order reduction of large circuits using balanced truncation","author":"Rabiei","year":"1999","journal-title":"Proceedings of the Asia and South Pacific Design Automation Conference"},{"issue":"11","key":"2026033114232718700_ref179","doi-asserted-by":"crossref","first-page":"1607","DOI":"10.1177\/1077546312474015","article-title":"Aeroelastic parameter identification in wind tunnel testing via the extended eigensystem realization algorithm","volume":"20","author":"Rebolho","year":"2014","journal-title":"Journal of Vibration and Control"},{"issue":"1","key":"2026033114232718700_ref180","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1080\/00207170903100214","article-title":"Positive real and bounded real balancing for model reduction of descriptor systems","volume":"83","author":"Reis","year":"2010","journal-title":"International Journal of Control"},{"issue":"2","key":"2026033114232718700_ref181","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1109\/TCAD.2002.806601","article-title":"A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices","volume":"22","author":"Rewienski","year":"2003","journal-title":"IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems"},{"issue":"10","key":"2026033114232718700_ref182","doi-asserted-by":"crossref","first-page":"1667","DOI":"10.1016\/S0005-1098(03)00167-5","article-title":"Time-delay systems: an overview of some recent advances and open problems","volume":"39","author":"Richard","year":"2003","journal-title":"Automatica"},{"issue":"9","key":"2026033114232718700_ref183","doi-asserted-by":"crossref","first-page":"2465","DOI":"10.1109\/TPEL.2011.2107920","article-title":"Unified general phasor transformation for AC converters","volume":"26","author":"Rim","year":"2011","journal-title":"IEEE Transactions on Power Electronics"},{"issue":"2","key":"2026033114232718700_ref184","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1109\/63.53157","article-title":"Phasor transformation and its application to the DC\/AC analyses of frequency phase-controlled series resonant converters (SRC)","volume":"5","author":"Rim","year":"1990","journal-title":"IEEE Transactions on Power Electronics"},{"issue":"3","key":"2026033114232718700_ref185","doi-asserted-by":"crossref","first-page":"1573","DOI":"10.1016\/j.apm.2008.02.008","article-title":"On the selection of the most adequate radial basis function","volume":"33","author":"Rocha","year":"2009","journal-title":"Applied Mathematical Modelling"},{"key":"2026033114232718700_ref186","doi-asserted-by":"crossref","first-page":"5121","DOI":"10.1109\/ACC.2005.1470832","article-title":"Adaptive partial state feedback control of the DC-to-DC \u0106uk converter","volume":"7","author":"Rodriguez","year":"2005","journal-title":"Proceedings of the 2005 American Control Conference"},{"issue":"1-2","key":"2026033114232718700_ref187","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.physd.2003.03.001","article-title":"Model reduction for compressible flows using POD and Galerkin projection","volume":"189","author":"Rowley","year":"2004","journal-title":"Physica D: Nonlinear Phenomena"},{"issue":"7","key":"2026033114232718700_ref188","doi-asserted-by":"crossref","first-page":"729","DOI":"10.1109\/9.29399","article-title":"A Schur method for balanced-truncation model reduction","volume":"34","author":"Safonov","year":"1989","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"4","key":"2026033114232718700_ref189","doi-asserted-by":"crossref","first-page":"496","DOI":"10.1109\/9.52314","article-title":"Optimal Hankel model reduction for nonminimal systems","volume":"35","author":"Safonov","year":"1990","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"3","key":"2026033114232718700_ref190","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1016\/j.jfranklin.2012.12.010","article-title":"Drilling vibration reduction via attractive ellipsoid method","volume":"350","author":"Saldivar","year":"2013","journal-title":"Journal of the Franklin Institute"},{"key":"2026033114232718700_ref191","first-page":"284","article-title":"Stick-slip oscillations in oillwell drilstrings: distributed parameter and neutral type retarded model approaches","author":"Saldivar","year":"2011"},{"key":"2026033114232718700_ref192","first-page":"4164","article-title":"Exponential stability analysis of the drilling system described by a switched neutral type delay equation with nonlinear perturbations","author":"Saldivar","year":"2011"},{"key":"2026033114232718700_ref193","article-title":"An overview on the modeling of oilwell drilling vibrations","author":"Salvidar","year":"2014"},{"issue":"3","key":"2026033114232718700_ref194","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1016\/j.automatica.2005.10.016","article-title":"A case study in model reduction of linear time-varying systems","volume":"42","author":"Sandberg","year":"2006","journal-title":"Automatica"},{"issue":"2","key":"2026033114232718700_ref195","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1109\/TAC.2003.822862","article-title":"Balanced truncation of linear time-varying systems","volume":"49","author":"Sandberg","year":"2004","journal-title":"IEEE Transactions on Automatic Control"},{"key":"2026033114232718700_ref196","first-page":"629","article-title":"Projection based fast passive compact macromodeling of high-speed VLSI circuits and interconnects","author":"Saraswat","year":"2005"},{"key":"2026033114232718700_ref197","first-page":"7310","article-title":"Model reduction for linear singular systems","author":"Scarciotti","year":"2015"},{"key":"2026033114232718700_ref198","first-page":"1","article-title":"Model reduction of power systems with preservation of slow and poorly damped modes","author":"Scarciotti","year":"2015"},{"key":"2026033114232718700_ref199","first-page":"7447","article-title":"Moment matching for nonlinear differential-algebraic equations","author":"Scarciotti","year":"2016"},{"issue":"1","key":"2026033114232718700_ref200","doi-asserted-by":"crossref","first-page":"743","DOI":"10.1109\/TPWRS.2016.2556747","article-title":"Low computational complexity model reduction of power systems with preservation of physical characteristics","volume":"32","author":"Scarciotti","year":"2017","journal-title":"IEEE Transactions on Power Systems"},{"key":"2026033114232718700_ref201","first-page":"1","article-title":"Discontinuous phasor model of an inductive power transfer system","author":"Scarciotti","year":"2017"},{"key":"2026033114232718700_ref202","article-title":"Steady-state matching and model reduction for systems of differential-algebraic equations","author":"Scarciotti","year":"2018","journal-title":"To appear on IEEE Transactions on Automatic Control"},{"key":"2026033114232718700_ref203","first-page":"9462","article-title":"Model reduction by moment matching for linear time-delay systems","author":"Scarciotti","year":"2014"},{"key":"2026033114232718700_ref204","first-page":"3642","article-title":"Model reduction by moment matching for nonlinear time-delay systems","author":"Scarciotti","year":"2014"},{"key":"2026033114232718700_ref205","first-page":"589","article-title":"Characterization of the moments of a linear system driven by explicit signal generators","author":"Scarciotti","year":"2015"},{"key":"2026033114232718700_ref206","first-page":"334","article-title":"Model reduction for linear systems and linear time-delay systems from input\/output data","author":"Scarciotti","year":"2015"},{"key":"2026033114232718700_ref207","first-page":"7298","article-title":"Model reduction for nonlinear systems and nonlinear time-delay systems from input\/output data","author":"Scarciotti","year":"2015"},{"issue":"6","key":"2026033114232718700_ref208","doi-asserted-by":"crossref","first-page":"1438","DOI":"10.1109\/TAC.2015.2461093","article-title":"Model reduction of neutral linear and nonlinear time-invariant time-delay systems with discrete and distributed delays","volume":"61","author":"Scarciotti","year":"2016","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"7","key":"2026033114232718700_ref209","doi-asserted-by":"crossref","first-page":"1995","DOI":"10.1109\/TAC.2015.2481838","article-title":"Model reduction by matching the steady-state response of explicit signal generators","volume":"61","author":"Scarciotti","year":"2016","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"12","key":"2026033114232718700_ref210","doi-asserted-by":"crossref","first-page":"8448","DOI":"10.1109\/TPEL.2016.2519382","article-title":"Moment-based discontinuous phasor transform and its application to the steady-state analysis of inverters and wireless power transfer systems","volume":"31","author":"Scarciotti","year":"2016","journal-title":"IEEE Transactions on Power Electronics"},{"key":"2026033114232718700_ref211","first-page":"7462","article-title":"A note on the electrical equivalent of the moment theory","author":"Scarciotti","year":"2016"},{"key":"2026033114232718700_ref212","first-page":"84","article-title":"Moments at \u201cdiscontinuous signals\u201d with applications: model reduction for hybrid systems and phasor transform for switching circuits","author":"Scarciotti","year":"2016"},{"key":"2026033114232718700_ref213","first-page":"862","article-title":"Model reduction for hybrid systems with statedependent jumps","author":"Scarciotti","year":"2016"},{"key":"2026033114232718700_ref214","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1016\/j.automatica.2017.01.014","article-title":"Data-driven model reduction by moment matching for linear and nonlinear systems","volume":"79","author":"Scarciotti","year":"2017","journal-title":"Automatica"},{"key":"2026033114232718700_ref215","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/978-3-319-51298-3_2","volume-title":"Feedback Stabilization of Controlled Dynamical Systems: In Honor of Laurent Praly","author":"Scarciotti","year":"2017"},{"key":"2026033114232718700_ref216","first-page":"6506","article-title":"Model order reduction of stochastic linear systems by moment matching","author":"Scarciotti","year":"2017"},{"key":"2026033114232718700_ref217","doi-asserted-by":"crossref","DOI":"10.1109\/CDC.2017.8264107","article-title":"Model order reduction for stochastic nonlinear systems","author":"Scarciotti","year":"2017"},{"key":"2026033114232718700_ref218","first-page":"7453","article-title":"Constrained optimal reduced-order models from input\/output data","author":"Scarciotti","year":"2016"},{"key":"2026033114232718700_ref219","article-title":"Data-driven constrained optimal model reduction","author":"Scarciotti","year":"2017","journal-title":"Submitted to Automatica"},{"key":"2026033114232718700_ref220","doi-asserted-by":"crossref","first-page":"3483","DOI":"10.23919\/ACC.2017.7963485","article-title":"Model reduction for linear differential inclusions: moment-set and time-variance","author":"Scarciotti","year":"2017","journal-title":"In Proceedings of the 2017 American Control Conference, Seattle"},{"issue":"2","key":"2026033114232718700_ref221","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/0167-6911(93)90117-O","article-title":"Balancing for nonlinear systems","volume":"21","author":"Scherpen","year":"1993","journal-title":"Systems & Control Letters"},{"issue":"11","key":"2026033114232718700_ref222","doi-asserted-by":"crossref","first-page":"2079","DOI":"10.1109\/9.887630","article-title":"Minimality and local state decompositions of a nonlinear state space realization using energy functions","volume":"45","author":"Scherpen","year":"2000","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"5","key":"2026033114232718700_ref223","doi-asserted-by":"crossref","first-page":"883","DOI":"10.1016\/S0362-546X(01)00867-7","article-title":"Nonlinear Hilbert adjoints: Properties and applications to Hankel singular value analysis","volume":"51","author":"Scherpen","year":"2002","journal-title":"Nonlinear Analysis: Theory, Methods & Applications"},{"issue":"6","key":"2026033114232718700_ref224","doi-asserted-by":"crossref","first-page":"1193","DOI":"10.1080\/00207179408921517","article-title":"Normalized coprime factorizations and balancing for unstable nonlinear systems","volume":"60","author":"Scherpen","year":"1994","journal-title":"International Journal of Control"},{"key":"2026033114232718700_ref225","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-5037-9","volume-title":"Dynamics of Evolutionary Equations","author":"Sell","year":"2002"},{"issue":"2","key":"2026033114232718700_ref226","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1090\/S0002-9947-1985-0783998-8","article-title":"Properties of center manifolds","volume":"289","author":"Sijbrand","year":"1985","journal-title":"Transactions of the American Mathematical Society"},{"key":"2026033114232718700_ref227","first-page":"712","article-title":"Model reduction of nonlinear differentialalgebraic equations","volume":"7","author":"Soberg","year":"2007","journal-title":"IFAC Symposium Nonlinear Control Systems, Pretoria, South Africa"},{"key":"2026033114232718700_ref228","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1016\/S0024-3795(02)00283-5","article-title":"The Sylvester equation and approximate balanced reduction","volume":"351","author":"Sorensen","year":"2002","journal-title":"Linear Algebra and its Applications"},{"key":"2026033114232718700_ref229","author":"St\u00e9p\u00e1n","year":"1989","journal-title":"Retarded Dynamical Systems: Stability and Characteristic Functions"},{"key":"2026033114232718700_ref230","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1007\/978-94-010-2675-8_15","volume-title":"Geometric Methods in System Theory: Proceedings of the NATO Advanced Study Institute held at London, England, August 27-September 7, 1973","author":"Sussmann","year":"1973"},{"issue":"4","key":"2026033114232718700_ref231","doi-asserted-by":"crossref","first-page":"1319","DOI":"10.1080\/00207178708933971","article-title":"Truncated balanced realization of a stable non-minimal state-space system","volume":"46","author":"Tombs","year":"1987","journal-title":"International Journal of Control"},{"key":"2026033114232718700_ref232","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-13812-6","volume-title":"Modeling and Identification of Linear Parameter-Varying Systems","author":"Toth","year":"2010"},{"issue":"12","key":"2026033114232718700_ref233","doi-asserted-by":"crossref","first-page":"1267","DOI":"10.1016\/j.aml.2007.09.015","article-title":"2-optimal model reduction of MIMO systems","volume":"21","author":"Van Dooren","year":"2008","journal-title":"Applied Mathematics Letters"},{"key":"2026033114232718700_ref234","first-page":"231","article-title":"Gramian based model reduction of large-scale dynamical systems","author":"Van Dooren","year":"2000","journal-title":"Chapman and Hall CRC Research Notes in Mathematics"},{"key":"2026033114232718700_ref235","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4613-0465-4","volume-title":"Subspace Identification for Linear Systems: Theory \u2013 Implementation \u2013 Applications","author":"van Overschee","year":"1996"},{"key":"2026033114232718700_ref236","first-page":"733","author":"Varga","year":"1992"},{"key":"2026033114232718700_ref237","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511618888","volume-title":"Filtering and System Identification: A Least Squares Approach","author":"Verhaegen","year":"2007"},{"key":"2026033114232718700_ref238","article-title":"Dynamics near limit cycles: Model reduction and sensitivity","author":"Verriest","year":"1998"},{"issue":"2","key":"2026033114232718700_ref239","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1016\/j.automatica.2008.08.017","article-title":"Adaptive optimal control for continuous-time linear systems based on policy iteration","volume":"45","author":"Vrabie","year":"2009","journal-title":"Automatica"},{"key":"2026033114232718700_ref240","first-page":"1826","article-title":"Online updating the generalized inverse of centered matrices","author":"Wang","year":"2011"},{"issue":"11","key":"2026033114232718700_ref241","doi-asserted-by":"crossref","first-page":"2323","DOI":"10.2514\/2.1570","article-title":"Balanced model reduction via the proper orthogonal decomposition","volume":"40","author":"Willcox","year":"2002","journal-title":"AIAA Journal"},{"key":"2026033114232718700_ref242","first-page":"1249","article-title":"Minimal representations for delay systems","author":"Yamamoto","year":"2008"},{"key":"2026033114232718700_ref243","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1109\/ASPDAC.2007.358011","article-title":"Passive interconnect macromodeling via balanced truncation of linear systems in descriptor form","author":"Yan","year":"2007","journal-title":"In 2007 Asia and South Pacific Design Automation Conference"},{"issue":"8","key":"2026033114232718700_ref244","doi-asserted-by":"crossref","first-page":"1103","DOI":"10.1109\/TCSI.2003.815227","article-title":"Small-signal analysis of frequency-controlled electronic ballasts","volume":"50","author":"Yin","year":"2003","journal-title":"IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications"},{"issue":"7","key":"2026033114232718700_ref245","doi-asserted-by":"crossref","first-page":"1008","DOI":"10.1109\/9.599985","article-title":"A new approximation method for time-delay systems","volume":"42","author":"Yoon","year":"1997","journal-title":"IEEE Transactions on Automatic Control"},{"key":"2026033114232718700_ref246","volume-title":"Linear System Theory: The State Space Approach","author":"Zadeh","year":"1963"},{"key":"2026033114232718700_ref247","first-page":"1458","article-title":"Stability of linear time-delay systems: a delay-dependent criterion with a tight conservatism bound","author":"Zhang","year":"2000"},{"issue":"12","key":"2026033114232718700_ref248","doi-asserted-by":"crossref","first-page":"1149","DOI":"10.1002\/rnc.834","article-title":"New results for the analysis of linear systems with time-invariant delays","volume":"13","author":"Zhang","year":"2003","journal-title":"International Journal of Robust and Nonlinear Control"},{"key":"2026033114232718700_ref249","volume-title":"Robust Control of Time-delay Systems","author":"Zhong","year":"2006"},{"issue":"3","key":"2026033114232718700_ref250","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1002\/(SICI)1099-1239(199903)9:3<183::AID-RNC399>3.0.CO;2-E","article-title":"Balanced realization and model reduction for unstable systems","volume":"9","author":"Zhou","year":"1999","journal-title":"International Journal of Robust and Nonlinear Control"}],"container-title":["Foundations and Trends\u00ae in Systems and Control"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.emerald.com\/ftsys\/article-pdf\/4\/3-4\/224\/11155021\/2600000012en.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/www.emerald.com\/ftsys\/article-pdf\/4\/3-4\/224\/11155021\/2600000012en.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T19:00:44Z","timestamp":1777489244000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.emerald.com\/ftsys\/article\/4\/3-4\/224\/1332409\/Nonlinear-Model-Reduction-by-Moment-Matching"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,8,8]]},"references-count":249,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2017,8,8]]}},"URL":"https:\/\/doi.org\/10.1561\/2600000012","relation":{},"ISSN":["2325-6818","2325-6826"],"issn-type":[{"value":"2325-6818","type":"print"},{"value":"2325-6826","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,8,8]]}}}