{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T06:19:03Z","timestamp":1773469143511,"version":"3.50.1"},"reference-count":42,"publisher":"Elsevier BV","issue":"2","license":[{"start":{"date-parts":[[2012,1,1]],"date-time":"2012-01-01T00:00:00Z","timestamp":1325376000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["European Journal of Control"],"published-print":{"date-parts":[[2012,1]]},"DOI":"10.3166\/ejc.18.122-132","type":"journal-article","created":{"date-parts":[[2012,8,3]],"date-time":"2012-08-03T12:28:52Z","timestamp":1343996932000},"page":"122-132","source":"Crossref","is-referenced-by-count":26,"title":["Stability Preservation in Projection-based Model Order Reduction of Large Scale Systems"],"prefix":"10.1016","volume":"18","author":[{"given":"Rosa Casta\u00f1\u00e9","family":"Selga","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Boris","family":"Lohmann","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rudy","family":"Eid","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.3166\/ejc.18.122-132_bib0005","unstructured":"Antoulas A, Sorensen D, Zhou Y. On the Decay Rate of Hankel Singular Values and Related Issues. Technical report Department of Computational and Applied Mathematics, Rice University, 2001."},{"key":"10.3166\/ejc.18.122-132_bib0010","article-title":"Approximation of Large-Scale Dynamical Systems","author":"Antoulas","year":"2005","journal-title":"SIAM Philadelphia"},{"key":"10.3166\/ejc.18.122-132_bib0015","unstructured":"Bai Z, Feldmann P, Freund R. Stable and Passive Reduced-Order Models Based on Partial Pad\u00e9 Approximation via the Lanczos Process. Numerical Analysis Manuscript 97\/3-10, Bell Laboratories, Lucent Technologies, November 1997."},{"key":"10.3166\/ejc.18.122-132_bib0020","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/s00607-006-0178-y","article-title":"Factorized Solution of Lyapunov Equations based on Hierarchical Matrix Arithmetic","volume":"78","author":"Baur","year":"2006","journal-title":"Computing"},{"issue":"10","key":"10.3166\/ejc.18.122-132_bib0025","doi-asserted-by":"crossref","first-page":"1466","DOI":"10.1109\/9.539427","article-title":"Model Reduction of Multi-Dimensional and Uncertain Systems","volume":"41","author":"Beck","year":"1996","journal-title":"IEEE Trans. Automat. Contr"},{"issue":"9","key":"10.3166\/ejc.18.122-132_bib0030","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1002\/nla.622","article-title":"Numerical Solution of Large Lyapunov Equations Riccati Equations, and Linear-quadratic Control Problems","volume":"15","author":"Benner","year":"2008","journal-title":"Numer. Linear Algebr"},{"key":"10.3166\/ejc.18.122-132_bib0035","first-page":"449","article-title":"SLICOT \u2013 A Subroutine Library in Systems and Control Theory","volume":"1","author":"Benner","year":"1999","journal-title":"Applied and Computational Control, Signals, and Circuits"},{"issue":"1","key":"10.3166\/ejc.18.122-132_bib0040","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1023\/A:1019191431273","article-title":"Solving Stable Generalized Lyapunov Equations with the Matrix Sign Function","volume":"20","author":"Benner","year":"1999","journal-title":"Numer Algorithms"},{"issue":"4","key":"10.3166\/ejc.18.122-132_bib0045","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1076\/mcmd.6.4.383.3658","article-title":"Balanced Truncation Model Reduction of Large Scale Dense Systems on Parallel Computers","volume":"6","author":"Benner","year":"2000","journal-title":"Math. Comput. Model. Dyn"},{"key":"10.3166\/ejc.18.122-132_bib0050","article-title":"A Collection of Benchmark Examples for Model Reduction of Linear Time Invariant Dynamical Systems","author":"Chahlaoui","year":"2002","journal-title":"Slicot working note"},{"key":"10.3166\/ejc.18.122-132_bib0055","unstructured":"Chen T-Y. Preconditioning Sparse Matrices for Computing Eigenvalues and Solving Linear Systems Equations. PhD Thesis, University of California, Berkeley, 2001."},{"issue":"1","key":"10.3166\/ejc.18.122-132_bib0060","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1007\/BF01437217","article-title":"On Matrix Norms and Logarithmic Norms","volume":"24","author":"Deutsch","year":"1975","journal-title":"Numer. Math"},{"key":"10.3166\/ejc.18.122-132_bib0065","unstructured":"Eid R. Time Domain Model Reduction by Moment Matching. PhD Thesis, Technische Universit\u00e4t M\u00fcnchen, Lehrstuhl f\u00fcr Regelungstechnik, 2009."},{"key":"10.3166\/ejc.18.122-132_bib0070","article-title":"Passive Reduced-order Modeling via Krylov-Subspace Methods","author":"Freund","year":"2000","journal-title":"Numerical Analysis Manuscripts"},{"key":"10.3166\/ejc.18.122-132_bib0075","article-title":"Passive Reduced-order Modeling via Krylov-Subspace Methods","author":"Freund","year":"2000","journal-title":"Numerical Analysis Manuscripts"},{"key":"10.3166\/ejc.18.122-132_bib0080","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1007\/s10107-006-0028-x","article-title":"Nonlinear Semidefinite Programming: Sensitivity, Convergence, and an Application in Passive Reduced-order Modeling","volume":"109","author":"Freund","year":"2007","journal-title":"Math. Program., Ser. B"},{"key":"10.3166\/ejc.18.122-132_bib0085","unstructured":"Grimme EJ. Krylov Projection Methods for Model Reduction. PhD thesis, Dep. of Electrical Eng., Uni. Illinois at Urbana Champaign, 1997."},{"key":"10.3166\/ejc.18.122-132_bib0090","doi-asserted-by":"crossref","first-page":"1964","DOI":"10.1016\/j.laa.2007.10.041","article-title":"An Iterative SVD-Krylov Based Method for Model Reduction of Large-scale Dynamical Systems","volume":"428","author":"Gugercin","year":"2008","journal-title":"Linear Algebra Appl"},{"key":"10.3166\/ejc.18.122-132_bib0095","series-title":"Proceedings of the Control and Decision Conference","article-title":"Interpolation-based H2 Model Reduction for port-Hamiltonian Systems","author":"Gugercin","year":"2009"},{"issue":"1","key":"10.3166\/ejc.18.122-132_bib0100","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1023\/A:1022205420182","article-title":"A Modified Low-Rank Smith Method for Large-Scale Lyapunov Equations","volume":"32","author":"Gugercin","year":"2003","journal-title":"Numer Algorithms"},{"key":"10.3166\/ejc.18.122-132_bib0105","doi-asserted-by":"crossref","first-page":"646","DOI":"10.1137\/S0895479897325955","article-title":"Logarithmic Norms for Matrix Pencils","volume":"20","author":"Higueras","year":"1999","journal-title":"SIAM J. Matrix Anal. A"},{"issue":"1","key":"10.3166\/ejc.18.122-132_bib0110","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/j.laa.2004.04.015","article-title":"The Weighted Logarithmic Matrix Norm and Bounds of the Matrix Exponential","volume":"390","author":"Hu","year":"2004","journal-title":"Linear Algebra Appl"},{"issue":"3","key":"10.3166\/ejc.18.122-132_bib0115","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 J. Matrix Anal. Appl"},{"key":"10.3166\/ejc.18.122-132_bib0120","unstructured":"Saak J. Efficient Numerical Solution of Large Scale Algebraic Matrix Equations in PDE Control and Model Order Reduction. PhD Thesis of the TU Chemnitz, 2009."},{"key":"10.3166\/ejc.18.122-132_bib0125","doi-asserted-by":"crossref","first-page":"839","DOI":"10.1109\/9.256362","article-title":"Vector Norms as Lyapunov Equations for Linear Systems","volume":"37","author":"Kiendl","year":"1992","journal-title":"IEEE Trans. Automat. Contr"},{"issue":"1","key":"10.3166\/ejc.18.122-132_bib0130","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/1322436.1322437","article-title":"Block Variants of Hammarling's Method for Solving Lyapunov Equations","volume":"34","author":"Kressner","year":"2008","journal-title":"ACM Trans. Math. Softw"},{"issue":"4","key":"10.3166\/ejc.18.122-132_bib0135","doi-asserted-by":"crossref","first-page":"693","DOI":"10.1137\/S0036144504443389","article-title":"Low-rank Solution of Lyapunov Equations","volume":"46","author":"Li","year":"2004","journal-title":"SIAM Review"},{"key":"10.3166\/ejc.18.122-132_bib0140","unstructured":"Lohmann B, Wolf T, Eid R, Kotyczka P. Passivity Preserving Order Reduction of Linear Port-Hamiltonian Systems by Moment Matching. Technical reports on automatic control, Lehrstuhl f\u00fcr Regelungstechnik, Technische Universit\u00e4t M\u00fcnchen, August 2009."},{"key":"10.3166\/ejc.18.122-132_bib0145","unstructured":"M\u00fcller PC. Stabilit\u00e4tserhaltende Ordnungsreduktion f\u00fcr Lineare Systeme: Anmerkungen un Erg\u00e4nzungen zu einem Vortrag von A. Yousefi und B. Lohmann am 28.09.2006. In GAMM-FA Dynamik und Regelungstheorie, W\u00fcrzburg, 04\/05\/2007 Germany, 2009."},{"key":"10.3166\/ejc.18.122-132_bib0150","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","author":"Moore","year":"1981","journal-title":"IEEE Trans. Automat. Contr"},{"key":"10.3166\/ejc.18.122-132_bib0155","doi-asserted-by":"crossref","first-page":"1055","DOI":"10.1016\/j.automatica.2006.02.005","article-title":"Preservation of Lyapunov Functions under Bilinear Mapping","volume":"42","author":"Mori","year":"2006","journal-title":"Automatica"},{"issue":"8","key":"10.3166\/ejc.18.122-132_bib0160","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 Trans. Comput. Aid. D"},{"issue":"4","key":"10.3166\/ejc.18.122-132_bib0165","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1145\/321043.321048","article-title":"On Pre-conditioning of Matrices","volume":"7","author":"Osborne","year":"1960","journal-title":"J. Assoc. Comput. Mach"},{"key":"10.3166\/ejc.18.122-132_bib0170","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1007\/BF02165404","article-title":"Balancing a Matrix for Calculation of Eigenvalues and Eigenvectors","volume":"13","author":"Parlett","year":"1969","journal-title":"Numer. Math"},{"issue":"4","key":"10.3166\/ejc.18.122-132_bib0175","doi-asserted-by":"crossref","first-page":"1401","DOI":"10.1137\/S1064827598347666","article-title":"A Cyclic Low-Rank Smith Method for Large Sparse Lyapunov Equations","volume":"21","author":"Penzl","year":"2000","journal-title":"SIAM J. Set Comput"},{"key":"10.3166\/ejc.18.122-132_bib0180","first-page":"4715","article-title":"Moment Matching for Linear Port-Hamiltonian Systems","author":"Rostyslav","year":"2009","journal-title":"Proceedings of the European Control Conference"},{"key":"10.3166\/ejc.18.122-132_bib0185","unstructured":"Salimbahrami B. Structure Preserving Order Reduction of Large Scale Second Order Models. PhD thesis, Institute of Automatic Control, Technische Universit\u00e4t M\u00fcnchen, 2005."},{"key":"10.3166\/ejc.18.122-132_bib0190","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1016\/j.sysconle.2004.07.006","article-title":"Passivity Preserving Model Reduction via Interpolation of Spectral Zeros","volume":"54","author":"Sorensen","year":"2005","journal-title":"Systems and Control Letters"},{"key":"10.3166\/ejc.18.122-132_bib0195","doi-asserted-by":"crossref","first-page":"741","DOI":"10.1137\/0712055","article-title":"On Logarithmic Norms","volume":"12","author":"Str\u00f6m","year":"1975","journal-title":"SIAM J. Numer. Anal"},{"key":"10.3166\/ejc.18.122-132_bib0200","doi-asserted-by":"crossref","first-page":"2141","DOI":"10.1080\/00207178708934040","article-title":"Model Reduction using a Projection Formulation","volume":"46","author":"Villemagne","year":"1987","journal-title":"Int. J. Contr"},{"key":"10.3166\/ejc.18.122-132_bib0205","unstructured":"Yousefi A. Preserving Stability in Model and Controller Reduction with Application to Embedded Systems. PhD Thesis, Technische Universit\u00e4t M\u00fcnchen, 2006."},{"key":"10.3166\/ejc.18.122-132_bib0210","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1155\/S0161171203202295","article-title":"Matrix Measure and Applications to Stability of Matrices and Interval Dynamical Systems","author":"Zahreddine","year":"2003","journal-title":"Int. J. Mathematics and Mathematical Sciences"}],"container-title":["European Journal of Control"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0947358012705344?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0947358012705344?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2018,11,21]],"date-time":"2018-11-21T18:25:52Z","timestamp":1542824752000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0947358012705344"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":42,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["S0947358012705344"],"URL":"https:\/\/doi.org\/10.3166\/ejc.18.122-132","relation":{},"ISSN":["0947-3580"],"issn-type":[{"value":"0947-3580","type":"print"}],"subject":[],"published":{"date-parts":[[2012,1]]}}}