Computation of the analytic center of the solution set of the linear matrix inequality arising in continuous- and discrete-time passivity analysis

dc.contributor.authorBankmann, Daniel
dc.contributor.authorMehrmann, Volker
dc.contributor.authorNesterov, Yurii
dc.contributor.authorVan Dooren, Paul
dc.date.accessioned2021-03-04T08:46:05Z
dc.date.available2021-03-04T08:46:05Z
dc.date.issued2020-07-23
dc.description.abstractIn this paper formulas are derived for the analytic center of the solution set of linear matrix inequalities (LMIs) defining passive transfer functions. The algebraic Riccati equations that are usually associated with such systems are related to boundary points of the convex set defined by the solution set of the LMI. It is shown that the analytic center is described by closely related matrix equations, and their properties are analyzed for continuous- and discrete-time systems. Numerical methods are derived to solve these equations via steepest descent and Newton methods. It is also shown that the analytic center has nice robustness properties when it is used to represent passive systems. The results are illustrated by numerical examples.en
dc.description.sponsorshipTU Berlin, Open-Access-Mittel – 2020en
dc.description.sponsorshipDFG, 361092219, Verteilte dynamische Netzsicherheitssteuerung in Elektroenergiesystemen der nächsten Generationen
dc.description.sponsorshipDFG, 239904186, TRR 154: Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzwerkenen
dc.identifier.eissn2305-2228
dc.identifier.issn2305-221X
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/12712
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-11512
dc.language.isoen
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subject.ddc510 Mathematiken
dc.subject.otheralgebraic Riccati equationen
dc.subject.otheranalytic centeren
dc.subject.otherlinear matrix inequalityen
dc.subject.otherpassivityen
dc.subject.otherpositive real systemen
dc.subject.otherrobustnessen
dc.titleComputation of the analytic center of the solution set of the linear matrix inequality arising in continuous- and discrete-time passivity analysisen
dc.typeArticleen
dc.type.versionpublishedVersionen
dcterms.bibliographicCitation.doi10.1007/s10013-020-00427-xen
dcterms.bibliographicCitation.issue4en
dcterms.bibliographicCitation.journaltitleVietnam Journal of Mathematicsen
dcterms.bibliographicCitation.originalpublishernameSpringerNatureen
dcterms.bibliographicCitation.originalpublisherplaceLondon [u.a.]en
dcterms.bibliographicCitation.pageend659en
dcterms.bibliographicCitation.pagestart633en
dcterms.bibliographicCitation.volume48en
tub.accessrights.dnbfreeen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften>Inst. Mathematik>FG Numerische Mathematikde
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.groupFG Numerische Mathematikde
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen
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