{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,28]],"date-time":"2026-08-28T18:45:13Z","timestamp":1787942713047,"version":"build-2784847793"},"reference-count":44,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Dyn. Syst."],"published-print":{"date-parts":[[2023,12,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>In this work, we present a novel data-driven method for identifying parametric MIMO generalized state-space or descriptor systems of low order that accurately capture the frequency and time domain behavior of large-scale linear dynamical systems. The low-order parametric descriptor systems are identified from transfer matrix samples by means of two-variable Lagrange rational matrix interpolation. This is done within the Loewner framework by deploying the new matrix-valued barycentric formula given in both right and left polynomial matrix fraction forms, which enables the construction of minimal parametric descriptor systems with rectangular transfer matrices. The developed method allows the reduction of order and parameter dependence complexity of the constructed system. Stability of the system is preserved by the postprocessing technique based on flipping signs of unstable poles. The developed methodology is illustrated with a few academic examples and applied to low-order parametric state-space identification of an aerodynamic system.<\/jats:p>","DOI":"10.1137\/22m1509898","type":"journal-article","created":{"date-parts":[[2023,11,21]],"date-time":"2023-11-21T08:01:08Z","timestamp":1700553668000},"page":"3130-3164","source":"Crossref","is-referenced-by-count":6,"title":["Low-Order Parametric State-Space Modeling of MIMO Systems in the Loewner Framework"],"prefix":"10.1137","volume":"22","author":[{"given":"Tea","family":"Vojkovic","sequence":"first","affiliation":[{"name":"Institute of Aeroelasticity, German Aerospace Center, 37073 G\u00f6ttingen, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David","family":"Quero","sequence":"additional","affiliation":[{"name":"Institute of Aeroelasticity, German Aerospace Center, 37073 G\u00f6ttingen, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9106-1893","authenticated-orcid":true,"given":"Charles","family":"Poussot-Vassal","sequence":"additional","affiliation":[{"name":"ONERA\/DTIS, Universit\u00e9 de Toulouse, F-31055 Toulouse, France."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6986-8447","authenticated-orcid":true,"given":"Pierre","family":"Vuillemin","sequence":"additional","affiliation":[{"name":"ONERA\/DTIS, Universit\u00e9 de Toulouse, F-31055 Toulouse, France."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,11,17]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(90)90140-8"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1093\/imamci\/3.2-3.61"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(90)90141-X"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2011.07.017"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1137\/15M1025426"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144502417715"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2022.3147034"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1109\/TMTT.2021.3136234"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1109\/TMTT.2008.924346"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2018.10.003"},{"key":"ref11","doi-asserted-by":"crossref","unstructured":"I. V. Gosea and A. C. Antoulas, Stability preserving post-processing methods applied in the Loewner framework, in 2016 IEEE 20th Workshop on Signal and Power Integrity (SPI), IEEE, 2016, pp. 1\u20134, https:\/\/doi.org\/10.1109\/SAPIW.2016.7496283.","DOI":"10.1109\/SaPIW.2016.7496283"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1137\/20M1324727"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1109\/TEMC.2017.2649100"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1109\/61.772353"},{"key":"ref15","doi-asserted-by":"crossref","unstructured":"A. Hochman, FastAAA: A fast rational-function fitter, in 2017 IEEE 26th Conference on Electrical Performance of Electronic Packaging and Systems (EPEPS), IEEE, 2017, pp. 1\u20133, https:\/\/doi.org\/10.1109\/EPEPS.2017.8329756.","DOI":"10.1109\/EPEPS.2017.8329756"},{"key":"ref16","unstructured":"A. C. Ionita, Lagrange Rational Interpolation and Its Applications to Approximation of Large-Scale Dynamical Systems, Ph.D. thesis, Rice University, 2013."},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1137\/130914619"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1109\/TMTT.2012.2222915"},{"key":"ref19","doi-asserted-by":"crossref","unstructured":"M. Kabir and R. Khazaka, Parametric macromodeling of high-speed modules from frequency-domain data using Loewner matrix based method, in 2013 IEEE MTT-S International Microwave Symposium Digest (MTT), IEEE, 2013, pp. 1\u20134, https:\/\/doi.org\/10.1109\/MWSYM.2013.6697352.","DOI":"10.1109\/MWSYM.2013.6697352"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1109\/LSP.2007.913583"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2013.11.012"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1109\/TCAD.2009.2034500"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.3182\/20110828-6-IT-1002.02651"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/draa098"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2007.03.008"},{"key":"ref26","doi-asserted-by":"crossref","unstructured":"P. Mlinari\u0107 and S. Gugercin, A Unifying Framework for Interpolatory \\(\\mathcal{L}_2\\)-Optimal Reduced-Order Modeling, preprint, arXiv:2209.00714, 2022.","DOI":"10.1137\/22M1516920"},{"key":"ref27","doi-asserted-by":"crossref","unstructured":"P. Mlinari\u0107 and S. Gugercin, \\(\\mathcal{L}_2\\)-Optimal Reduced-Order Modeling Using Parameter-Separable Forms, preprint, arXiv:2206.02929, 2022.","DOI":"10.1137\/22M1500678"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1137\/16M1106122"},{"key":"ref29","unstructured":"L. R. Petzold, Description of DASSL: A Differential\/Algebraic System Solver, Technical report, Sandia National Labs, Livermore, CA, 1982."},{"key":"ref30","unstructured":"A. Roberts, Differential Algebraic Equation Solvers, 1998, https:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/28-differential-algebraic-equation-solvers."},{"key":"ref31","doi-asserted-by":"crossref","unstructured":"A. C. Rodriguez, L. Balicki, and S. Gugercin, The p-AAA Algorithm for Data Driven Modeling of Parametric Dynamical Systems, preprint, arXiv:2003.06536, 2022.","DOI":"10.1137\/20M1322698"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2021.3110809"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1007\/s00498-004-0141-4"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1109\/TEMC.2010.2043256"},{"key":"ref35","doi-asserted-by":"crossref","unstructured":"P. Triverio, S. Grivet-Talocia, and M. S. Nakhla, An improved fitting algorithm for parametric macromodeling from tabulated data, in 2008 12th IEEE Workshop on Signal Propagation on Interconnects, IEEE, 2008, pp. 1\u20134, https:\/\/doi.org\/10.1109\/SPI.2008.4558379.","DOI":"10.1109\/SPI.2008.4558379"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1109\/EPEP.2007.4387121"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1981.1102763"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1016\/j.ifacol.2022.09.087"},{"key":"ref39","doi-asserted-by":"crossref","unstructured":"Y. Wang, C.U. Lei, G. K. Pang, and N. Wong, MFTI: Matrix-format tangential interpolation for modeling multi-port systems, in Proceedings of the 47th Design Automation Conference, ACM, 2010, pp. 683\u2013686, https:\/\/doi.org\/10.1145\/1837274.1837447.","DOI":"10.1145\/1837274.1837447"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1186\/s40323-019-0134-y"},{"key":"ref41","doi-asserted-by":"crossref","unstructured":"A. Zanco and S. Grivet-Talocia, High-dimensional parameterized macromodeling with guaranteed stability, in 2019 IEEE 28th Conference on Electrical Performance of Electronic Packaging and Systems (EPEPS), IEEE, 2019, pp. 1\u20133, https:\/\/doi.org\/10.1109\/EPEPS47316.2019.193203.","DOI":"10.1109\/EPEPS47316.2019.193203"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1109\/TCPMT.2021.3099958"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1109\/TCAD.2018.2883962"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1109\/TCPMT.2020.3012275"}],"container-title":["SIAM Journal on Applied Dynamical Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/22M1509898","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T12:20:03Z","timestamp":1787228403000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/22M1509898"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,17]]},"references-count":44,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2023,12,31]]}},"alternative-id":["10.1137\/22M1509898"],"URL":"https:\/\/doi.org\/10.1137\/22m1509898","relation":{},"ISSN":["1536-0040"],"issn-type":[{"value":"1536-0040","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,11,17]]}}}