Structure-preserving interpolation of bilinear control systems

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dc.contributor.authorBenner, Peteren
dc.contributor.authorGugercin, Serkanen
dc.contributor.authorWerner, Steffen W. R.en
dc.contributor.departmentMathematicsen
dc.contributor.departmentAcademy of Integrated Scienceen
dc.date.accessioned2021-07-27T12:35:49Zen
dc.date.available2021-07-27T12:35:49Zen
dc.date.issued2021-06en
dc.description.abstractIn this paper, we extend the structure-preserving interpolatory model reduction framework, originally developed for linear systems, to structured bilinear control systems. Specifically, we give explicit construction formulae for the model reduction bases to satisfy different types of interpolation conditions. First, we establish the analysis for transfer function interpolation for single-input single-output structured bilinear systems. Then, we extend these results to the case of multi-input multi-output structured bilinear systems by matrix interpolation. The effectiveness of our structure-preserving approach is illustrated by means of various numerical examples.en
dc.description.notesOpen Access funding enabled and organized by Projekt DEAL. Benner and Werner were supported by the German Research Foundation (DFG) Research Training Group 2297 "MathCoRe," Magdeburg, and the German Research Foundation (DFG) Priority Program 1897: "Calm, Smooth and Smart - Novel Approaches for Influencing Vibrations by Means of Deliberately Introduced Dissipation." Gugercin was supported in parts by National Science Foundation under Grant No. DMS-1720257 and DMS-1819110. Part of this material is based upon work supported by the National Science Foundation under Grant No. DMS-1439786 and by the Simons Foundation Grant No. 50736 while Gugercin and Benner were in residence at the Institute for Computational and Experimental Research in Mathematics in Providence, RI, during the "Model and dimension reduction in uncertain and dynamic systems" program.en
dc.description.sponsorshipGerman Research Foundation (DFG)German Research Foundation (DFG) [2297, 1897]; National Science FoundationNational Science Foundation (NSF) [DMS-1439786, DMS-1720257, DMS-1819110]; Simons Foundation [50736]; Projekt DEALen
dc.description.versionPublished versionen
dc.format.mimetypeapplication/pdfen
dc.identifier.doihttps://doi.org/10.1007/s10444-021-09863-wen
dc.identifier.eissn1572-9044en
dc.identifier.issn1019-7168en
dc.identifier.issue3en
dc.identifier.other43en
dc.identifier.urihttp://hdl.handle.net/10919/104405en
dc.identifier.volume47en
dc.language.isoenen
dc.rightsCreative Commons Attribution 4.0 Internationalen
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/en
dc.subjectModel reductionen
dc.subjectBilinear systemsen
dc.subjectStructure-preserving approximationen
dc.subjectStructured interpolationen
dc.titleStructure-preserving interpolation of bilinear control systemsen
dc.title.serialAdvances in Computational Mathematicsen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten
dc.type.dcmitypeStillImageen

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