Please use this identifier to cite or link to this item: http://dx.doi.org/10.14279/depositonce-14225
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Main Title: A general framework for the perturbation theory of matrix equations
Author(s): Konstantinov, Mihail
Mehrmann, Volker
Petkov, Petko
Gu, Dawei
Type: Research Paper
URI: https://depositonce.tu-berlin.de/handle/11303/15452
http://dx.doi.org/10.14279/depositonce-14225
License: http://rightsstatements.org/vocab/InC/1.0/
Abstract: A general framework is presented for the local and non-local perturbation analysis of general real and complex matrix equations in the form $F(P,X) = 0$, where $F$ is a continuous, matrix valued function, $P$ is a collection of matrix parameters and $X$ is the unknown matrix. The local perturbation analysis produces condition numbers and improved first order homogeneous perturbation bounds for the norm $\|\de X\|$ or the absolute value $|\de X|$ of $\de X$. The non-local perturbation analysis is based on the method of Lyapunov majorants and fixed point principles. % for the operator $\pi(p,\cdot)$. It gives rigorous non-local perturbation bounds as well as conditions for solvability of the perturbed equation. The general framework can be applied to various matrix perturbation problems in science and engineering. We illustrate the procedure with several simple examples. Furhermore, as a model problem for the new framework we derive a new perturbation theory for continuous-time algebraic matrix Riccati equations in descriptor form, $Q + A^HXE + E^HXA - E^HXSXE = 0$. The associated equation $Q + A^HXE + E^HX^HA - E^HX^HSXE = 0$ is also briefly considered.
Subject(s): perturbation analysis
general matrix equations
descriptor Riccati equations
Issue Date: 6-Dec-2002
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 15A24 Matrix equations and identities
93C73 Perturbations
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2002, 760
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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