Approximation of stability radii for large-scale dissipative Hamiltonian systems

dc.contributor.authorAliyev, Nicat
dc.contributor.authorMehrmann, Volker
dc.contributor.authorMengi, Emre
dc.date.accessioned2021-03-12T07:39:13Z
dc.date.available2021-03-12T07:39:13Z
dc.date.issued2020-02-06
dc.description.abstractA linear time-invariant dissipative Hamiltonian (DH) system x ̇ = ( J − R ) Q x, with a skew-Hermitian J , a Hermitian positive semidefinite R , and a Hermitian positive definite Q , is always Lyapunov stable and under further weak conditions even asymptotically stable. By exploiting the characterizations from Mehl et al. (SIAM J. Matrix Anal. Appl. 37 (4), 1625–1654, 2016 ), we focus on the estimation of two stability radii for large-scale DH systems, one with respect to non-Hermitian perturbations of R in the form R + B Δ C H for given matrices B , C , and another with respect to Hermitian perturbations in the form R + B Δ B H ,Δ = Δ H . We propose subspace frameworks for both stability radii that converge at a superlinear rate in theory. The one for the non-Hermitian stability radius benefits from the DH structure-preserving model order reduction techniques, whereas for the Hermitian stability radius we derive subspaces yielding a Hermite interpolation property between the full and projected problems. With the proposed frameworks, we are able to estimate the two stability radii accurately and efficiently for large-scale systems which include a finite-element model of an industrial disk brake.en
dc.description.sponsorshipTU Berlin, Open-Access-Mittel – 2020en
dc.description.sponsorshipDFG, 273845692, SPP 1897: Calm, Smooth and Smart - Novel Approaches for Influencing Vibrations by Means of Deliberately Introduced Dissipationen
dc.identifier.eissn1572-9044
dc.identifier.issn1019-7168
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/12814
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-11614
dc.language.isoen
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subject.ddc510 Mathematiken
dc.subject.otherdissipative hamiltonian systemen
dc.subject.othereigenvalue optimizationen
dc.subject.otherhermite interpolationen
dc.subject.otherrobust stabilityen
dc.subject.otherstability radiusen
dc.subject.otherstructure-preserving subspace frameworken
dc.subject.othersubspace projectionen
dc.titleApproximation of stability radii for large-scale dissipative Hamiltonian systemsen
dc.typeArticleen
dc.type.versionpublishedVersionen
dcterms.bibliographicCitation.articlenumber6en
dcterms.bibliographicCitation.doi10.1007/s10444-020-09763-5en
dcterms.bibliographicCitation.issue1en
dcterms.bibliographicCitation.journaltitleAdvances in Computational Mathematicsen
dcterms.bibliographicCitation.originalpublishernameSpringerNatureen
dcterms.bibliographicCitation.originalpublisherplaceLondon [u.a.]en
dcterms.bibliographicCitation.volume46en
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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