Model reduction of descriptor systems by interpolatory projection methods

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dc.contributor.authorGugercin, Serkanen
dc.contributor.authorStykel, T.en
dc.contributor.authorWyatt, S.en
dc.contributor.departmentMathematicsen
dc.date.accessed2014-05-27en
dc.date.accessioned2014-05-28T18:35:10Zen
dc.date.available2014-05-28T18:35:10Zen
dc.date.issued2013en
dc.description.abstractIn this paper, we investigate an interpolatory projection framework for model reduction of descriptor systems. With a simple numerical example, we first illustrate that directly applying the subspace conditions from the standard state space settings to descriptor systems generically leads to unbounded H-2 or H-infinity errors due to the mismatch of the polynomial parts of the full and reduced-order transfer functions. We then develop modified interpolatory subspace conditions based on the deflating subspaces that guarantee a bounded error. For the special cases of index-1 and index-2 descriptor systems, we also show how to avoid computing these deflating subspaces explicitly while still enforcing interpolation. The question of how to choose interpolation points optimally naturally arises as in the standard state space setting. We answer this question in the framework of the H-2-norm by extending the iterative rational Krylov algorithm to descriptor systems. Several numerical examples are used to illustrate the theoretical discussion.en
dc.description.sponsorshipNSF DMS-0645347en
dc.description.sponsorshipResearch Network FROPT: Model Reduction Based Optimal Control for Field-Flow Fractionationen
dc.description.sponsorshipGerman Federal Ministry of Education and Science (BMBF) 05M10WABen
dc.format.mimetypeapplication/pdfen
dc.identifier.citationGugercin, S.; Stykel, T.; Wyatt, S., "Model reduction of descriptor systems by interpolatory projection methods," SIAM J. Sci. Comput., 35(5), B1010-B1033, (2013). DOI: 10.1137/130906635en
dc.identifier.doihttps://doi.org/10.1137/130906635en
dc.identifier.issn1064-8275en
dc.identifier.urihttp://hdl.handle.net/10919/48159en
dc.identifier.urlhttp://epubs.siam.org/doi/abs/10.1137/130906635en
dc.language.isoenen
dc.publisherSiam Publicationsen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectinterpolatory model reductionen
dc.subjectdifferential-algebraic equationsen
dc.subjecth-2en
dc.subjectapproximationen
dc.subjectequationsen
dc.subjectapproximationen
dc.subjectrealizationen
dc.subjectmathematics, applieden
dc.titleModel reduction of descriptor systems by interpolatory projection methodsen
dc.title.serialSiam Journal on Scientific Computingen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten

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