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

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dc.contributor.authorBankmann, Daniel
dc.contributor.authorMehrmann, Volker
dc.contributor.authorNesterov, Yurii
dc.contributor.authorVan Dooren, Paul
dc.date.accessioned2021-12-17T10:15:59Z
dc.date.available2021-12-17T10:15:59Z
dc.date.issued2019-04-17
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 ascent and Newton-like 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.identifier.issn2197-8085
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/15918
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-14691
dc.language.isoenen
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.ddc510 Mathematiken
dc.subject.otherLinear matrix inequalityen
dc.subject.otheranalytic centeren
dc.subject.otherpassivityen
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.typeResearch Paperen
dc.type.versionsubmittedVersionen
tub.accessrights.dnbfreeen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften::Inst. Mathematikde
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen
tub.series.issuenumber2019, 06en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
tub.subject.msc200093D09 Robust stabilityen
tub.subject.msc200049M15 Methods of Newton-Raphson, Galerkin and Ritz typesen

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