Computing nearest stable matrix pairs
| dc.contributor.author | Gillis, Nicolas | |
| dc.contributor.author | Mehrmann, Volker | |
| dc.contributor.author | Sharma, Punit | |
| dc.date.accessioned | 2021-12-17T10:15:09Z | |
| dc.date.available | 2021-12-17T10:15:09Z | |
| dc.date.issued | 2017-04-12 | |
| dc.description.abstract | In this paper, we study the nearest stable matrix pair problem: given a square matrix pair (E,A), minimize the Frobenius norm of (∆E,∆A) such that (E+\∆E,A+∆A) is a stable matrix pair. We propose a reformulation of the problem with a simpler feasible set byintroducing dissipative Hamiltonian (DH) matrix pairs: A matrix pair (E,A) is DH if A=(J-R)Q with skew-symmetric J, positive semidefinite R, and an invertible Q such that Q^TE is positive semidefinite. This reformulation has a convex feasible domain onto which it is easy to project. This allows us to employ a fast gradient method to obtain a nearby stable approximation of a given matrix pair. | en |
| dc.identifier.issn | 2197-8085 | |
| dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/15895 | |
| dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-14668 | |
| dc.language.iso | en | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject.ddc | 510 Mathematik | en |
| dc.subject.other | dissipative Hamiltonian system | en |
| dc.subject.other | distance to stability | en |
| dc.subject.other | convex optimization | en |
| dc.title | Computing nearest stable matrix pairs | en |
| dc.type | Research Paper | en |
| dc.type.version | submittedVersion | en |
| tub.accessrights.dnb | free | en |
| tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik | de |
| tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
| tub.affiliation.institute | Inst. Mathematik | de |
| tub.publisher.universityorinstitution | Technische Universität Berlin | en |
| tub.series.issuenumber | 2017, 04 | en |
| tub.series.name | Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin | en |
| tub.subject.msc2000 | 93D09 Robust stability | en |
| tub.subject.msc2000 | 65F15 Eigenvalues, eigenvectors | en |
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