{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:33:48Z","timestamp":1787337228180,"version":"build-2736575974"},"reference-count":25,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[2015,1]]},"abstract":"<jats:p>In this paper, we focus on model reduction of large-scale bilinear systems. The main contributions are threefold. First, we introduce a new framework for interpolatory model reduction of bilinear systems. In contrast to the existing methods where interpolation is forced on some of the leading subsystem transfer functions, the new framework shows how to enforce multipoint interpolation of the underlying Volterra series. Then, we show that the first-order conditions for optimal $\\mathcal{H}_2$ model reduction of bilinear systems require multivariate Hermite interpolation in terms of the new Volterra series interpolation framework; thus we extend the interpolation-based first-order necessary conditions for $\\mathcal{H}_2$ optimality of LTI systems to the bilinear case. Finally, we show that multipoint interpolation on the truncated Volterra series representation of a bilinear system leads to an asymptotically optimal approach to $\\mathcal{H}_2$ optimal model reduction, leading to an efficient model reduction algorithm. Several numerical examples illustrate the effectiveness of the proposed approach.<\/jats:p>","DOI":"10.1137\/130947830","type":"journal-article","created":{"date-parts":[[2015,5,19]],"date-time":"2015-05-19T12:23:51Z","timestamp":1432038231000},"page":"549-579","source":"Crossref","is-referenced-by-count":69,"title":["Multipoint Volterra Series Interpolation and $\\mathcal{H}_2$ Optimal Model Reduction of Bilinear Systems"],"prefix":"10.1137","volume":"36","author":[{"given":"Garret","family":"Flagg","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Serkan","family":"Gugercin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,5,19]]},"reference":[{"key":"atypb1","doi-asserted-by":"crossref","unstructured":"A.C. Antoulas,\n                      Approximation of Large-Scale Dynamical Systems\n                      Adv. Des. Control 6, SIAM, Philadelphia, 2005.","DOI":"10.1137\/1.9780898718713"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2005.04.032"},{"key":"atypb3","first-page":"199","author":"Beatson R.K.","year":"2007","journal-title":"Berlin"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1002\/pamm.201110391"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1137\/110836742"},{"key":"atypb6","first-page":"153","author":"Benner P.","year":"2012","journal-title":"Heidelberg"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1137\/09075041X"},{"key":"atypb8","unstructured":"P. Benner, M. K\u00f6hler, and J. Saak,\n                      Sparse-dense Sylvester equations in $\\mathcal{H}_2$-model order reduction\n                      , Tech. report, Max Planck Institute, Madgeburg, Germany, 2011."},{"key":"atypb9","unstructured":"T. Breiten,\n                      Krylov Subspace Methods for Model Order Reduction of Bilinear Control Systems\n                      , master's thesis, Department of Mathematics, Technical University of Kaiserslautern, Kaiserslautern, Germany, 2009."},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2010.06.003"},{"key":"atypb11","unstructured":"G.M. Flagg,\n                      Interpolation Methods for the Model Reduction of Bilinear Systems\n                      , Ph.D. thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA, 2012."},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2012.03.005"},{"key":"atypb13","unstructured":"S. Gugercin,\n                      Projection Methods for Model Reduction of Large-Scale Dynamical Systems\n                      , Ph.D. thesis, Ph.D. Dissertation, ECE Dept., Rice University, Houston, TX, 2002."},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1137\/060666123"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1137\/100796844"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1967.1098680"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1109\/TSSC.1970.300341"},{"key":"atypb18","unstructured":"R.R. Mohler,\n                      Nonlinear Systems (Vol. 2): Applications to Bilinear Control\n                      , Prentice-Hall, Inc., Upper Saddle River, NJ, 1991."},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1109\/TCAD.2002.806605"},{"key":"atypb20","unstructured":"W.J. 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Spina,\n                      Sinusoidal Analysis and Modeling of Weakly Nonlinear Circuits: With Application to Nonlinear Interference Effects\n                      , Van Nostrand Reinhold, New York, 1980."},{"key":"atypb24","first-page":"1161","volume":"117","author":"Wilson D.A.","year":"1970","journal-title":"IEEE Proceedings"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1016\/S0005-1098(01)00204-7"}],"container-title":["SIAM Journal on Matrix Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/130947830","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:50:58Z","timestamp":1787334658000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/130947830"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1]]},"references-count":25,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2015,1]]}},"alternative-id":["10.1137\/130947830"],"URL":"https:\/\/doi.org\/10.1137\/130947830","relation":{},"ISSN":["0895-4798","1095-7162"],"issn-type":[{"value":"0895-4798","type":"print"},{"value":"1095-7162","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,1]]}}}