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Main Title: Perturbation theory for Hamiltonian matrices and the distance to bounded-realness
Author(s): Alam, Rafikul
Bora, Shreemayee
Karow, Michael
Mehrmann, Volker
Moro, Julio
Type: Article
Language Code: en
Abstract: Motivated by the analysis of passive control systems, we undertake a detailed perturbation analysis of Hamiltonian matrices that have eigenvalues on the imaginary axis. We construct minimal Hamiltonian perturbations that move and coalesce eigenvalues of opposite sign characteristic to form multiple eigenvalues with mixed sign characteristics, which are then moved from the imaginary axis to specific locations in the complex plane by small Hamiltonian perturbations. We also present a numerical method to compute upper bounds for the minimal perturbations that move all eigenvalues of a given Hamiltonian matrix outside a vertical strip along the imaginary axis.
Issue Date: 27-Jun-2011
Date Available: 14-Dec-2017
DDC Class: DDC::500 Naturwissenschaften und Mathematik::510 Mathematik::519 Wahrscheinlichkeiten, angewandte Mathematik
DDC::500 Naturwissenschaften und Mathematik::510 Mathematik::518 Numerische Analysis
Subject(s): Hamiltonian matrix
Hamiltonian eigenvalue problem
structured mapping problem
distance to bounded-realness
perturbation theory
passive system
purely imaginary eigenvalues
sign characteristic
Hamiltonian pseudospectra
Usage rights: Terms of German Copyright Law
Journal Title: SIAM Journal on Matrix Analysis and Applications
Publisher: Society for Industrial and Applied Mathematics
Publisher Place: Philadelphia, Pa.
Volume: 32
Issue: 2
Publisher DOI: 10.1137/10079464X
Page Start: 484
Page End: 514
EISSN: 1095-7162
ISSN: 0895-4798
Appears in Collections:Fachgebiet Numerische Lineare Algebra » Publications

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