Publication:
Approximation of stability radii for large-scale dissipative Hamiltonian systems

dc.contributor.coauthorAliyev, Nicat
dc.contributor.coauthorMehrmann, Volker
dc.contributor.departmentDepartment of Mathematics
dc.contributor.kuauthorMengi, Emre
dc.contributor.schoolcollegeinstituteCollege of Sciences
dc.date.accessioned2024-11-09T13:22:05Z
dc.date.issued2020
dc.description.abstractA linear time-invariant dissipative Hamiltonian (DH) system (x) over dot = (J-R)Qx, 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 Delta C-H for given matrices B, C, and another with respect to Hermitian perturbations in the form R + B Delta B-H, Delta = Delta(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.
dc.description.fulltextYES
dc.description.indexedbyWOS
dc.description.indexedbyScopus
dc.description.issue1
dc.description.openaccessYES
dc.description.publisherscopeInternational
dc.description.sponsoredbyTubitakEuN/A
dc.description.sponsorshipDeutsche Forschungsgemeinschaft, Project ME 40-1 of Priority Program 1897, Calm, Smooth and Smart
dc.description.sponsorshipDeutsche Forschungsgemeinschaft, Project A02 of Sonderforschungsbereich 910
dc.description.versionPublisher version
dc.description.volume46
dc.identifier.doi10.1007/s10444-020-09763-5
dc.identifier.eissn1572-9044
dc.identifier.embargoNO
dc.identifier.filenameinventorynoIR02091
dc.identifier.issn1019-7168
dc.identifier.quartileQ2
dc.identifier.scopus2-s2.0-85079184551
dc.identifier.urihttps://doi.org/10.1007/s10444-020-09763-5
dc.identifier.wos512837400001
dc.keywordsDissipative hamiltonian system
dc.keywordsRobust stability
dc.keywordsStability radius
dc.keywordsEigenvalue optimization
dc.keywordsSubspace projection
dc.keywordsStructure-preserving subspace framework
dc.keywordsHermite interpolation
dc.language.isoeng
dc.publisherSpringer
dc.relation.grantnoNA
dc.relation.ispartofAdvances in Computational Mathematics
dc.relation.urihttp://cdm21054.contentdm.oclc.org/cdm/ref/collection/IR/id/8729
dc.subjectMathematics, applied
dc.titleApproximation of stability radii for large-scale dissipative Hamiltonian systems
dc.typeJournal Article
dspace.entity.typePublication
local.contributor.kuauthorMengi, Emre
local.publication.orgunit1College of Sciences
local.publication.orgunit2Department of Mathematics
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