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Main Title: Computing nearest stable matrix pairs
Author(s): Gillis, Nicolas
Mehrmann, Volker
Sharma, Punit
Type: Research Paper
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.
Subject(s): dissipative Hamiltonian system
distance to stability
convex optimization
Issue Date: 12-Apr-2017
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 93D09 Robust stability
65F15 Eigenvalues, eigenvectors
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2017, 04
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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