Please use this identifier to cite or link to this item:
http://dx.doi.org/10.14279/depositonce-6550
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. |
URI: | https://depositonce.tu-berlin.de//handle/11303/7277 http://dx.doi.org/10.14279/depositonce-6550 |
Issue Date: | 27-Jun-2011 |
Date Available: | 14-Dec-2017 |
DDC Class: | 519 Wahrscheinlichkeiten, angewandte Mathematik 518 Numerische Analysis |
Subject(s): | Hamiltonian matrix Hamiltonian eigenvalue problem structured mapping problem distance to bounded-realness perturbation theory passive system bounded-realness purely imaginary eigenvalues sign characteristic Hamiltonian pseudospectra |
License: | http://rightsstatements.org/vocab/InC/1.0/ |
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: | FG Numerische Lineare Algebra » Publications |
Files in This Item:
File | Description | Size | Format | |
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2011_karow_et-al.pdf | 729.91 kB | Adobe PDF | ![]() View/Open |
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