Computation of the analytic center of the solution set of the linear matrix inequality arising in continuous- and discrete-time passivity analysis
dc.contributor.author | Bankmann, Daniel | |
dc.contributor.author | Mehrmann, Volker | |
dc.contributor.author | Nesterov, Yurii | |
dc.contributor.author | Van Dooren, Paul | |
dc.date.accessioned | 2021-03-04T08:46:05Z | |
dc.date.available | 2021-03-04T08:46:05Z | |
dc.date.issued | 2020-07-23 | |
dc.description.abstract | In 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.sponsorship | TU Berlin, Open-Access-Mittel – 2020 | en |
dc.description.sponsorship | DFG, 361092219, Verteilte dynamische Netzsicherheitssteuerung in Elektroenergiesystemen der nächsten Generation | en |
dc.description.sponsorship | DFG, 239904186, TRR 154: Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzwerken | en |
dc.identifier.eissn | 2305-2228 | |
dc.identifier.issn | 2305-221X | |
dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/12712 | |
dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-11512 | |
dc.language.iso | en | |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
dc.subject.ddc | 510 Mathematik | en |
dc.subject.other | algebraic Riccati equation | en |
dc.subject.other | analytic center | en |
dc.subject.other | linear matrix inequality | en |
dc.subject.other | passivity | en |
dc.subject.other | positive real system | en |
dc.subject.other | robustness | en |
dc.title | Computation of the analytic center of the solution set of the linear matrix inequality arising in continuous- and discrete-time passivity analysis | en |
dc.type | Article | en |
dc.type.version | publishedVersion | en |
dcterms.bibliographicCitation.doi | 10.1007/s10013-020-00427-x | en |
dcterms.bibliographicCitation.issue | 4 | en |
dcterms.bibliographicCitation.journaltitle | Vietnam Journal of Mathematics | en |
dcterms.bibliographicCitation.originalpublishername | SpringerNature | en |
dcterms.bibliographicCitation.originalpublisherplace | London [u.a.] | en |
dcterms.bibliographicCitation.pageend | 659 | en |
dcterms.bibliographicCitation.pagestart | 633 | en |
dcterms.bibliographicCitation.volume | 48 | en |
tub.accessrights.dnb | free | en |
tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik::FG Numerische Mathematik | de |
tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
tub.affiliation.group | FG Numerische Mathematik | de |
tub.affiliation.institute | Inst. Mathematik | de |
tub.publisher.universityorinstitution | Technische Universität Berlin | en |
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