Please use this identifier to cite or link to this item: http://dx.doi.org/10.14279/depositonce-11614
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Main Title: Approximation of stability radii for large-scale dissipative Hamiltonian systems
Author(s): Aliyev, Nicat
Mehrmann, Volker
Mengi, Emre
Type: Article
URI: https://depositonce.tu-berlin.de/handle/11303/12814
http://dx.doi.org/10.14279/depositonce-11614
License: https://creativecommons.org/licenses/by/4.0/
Abstract: A 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.
Subject(s): dissipative hamiltonian system
eigenvalue optimization
hermite interpolation
robust stability
stability radius
structure-preserving subspace framework
subspace projection
Issue Date: 6-Feb-2020
Date Available: 12-Mar-2021
Language Code: en
DDC Class: 510 Mathematik
Sponsor/Funder: TU Berlin, Open-Access-Mittel – 2020
DFG, 273845692, SPP 1897: Calm, Smooth and Smart - Novel Approaches for Influencing Vibrations by Means of Deliberately Introduced Dissipation
Journal Title: Advances in Computational Mathematics
Publisher: SpringerNature
Volume: 46
Issue: 1
Article Number: 6
Publisher DOI: 10.1007/s10444-020-09763-5
EISSN: 1572-9044
ISSN: 1019-7168
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik » FG Numerische Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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