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Second Conference on Numerical Analysis and Applications
June 11-15, 2000
University of Rousse
Rousse, Bulgaria

Organizers
Plamen Yalamov, Marcin Paprzycki, Lubin Vulkov

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Sensitivity Analysis of Generalized Lyapunov Equations
by
M.M. Konstantinov
University of Architecture and Civil Engineering, Sofia, Bulgaria
Coauthors: P.Hr. Petkov, N.D. Christov, A. Barraud, S. Lesecq

{\Large Sensitivity Analysis of Generalized Lyapunov Equations}

Sensitivity Analysis of Generalized Lyapunov Equations

M.M. KONSTANTINOV*     P.HR. PETKOV**     N.D. CHRISTOV**
A. BARRAUD***     S. LESECQ***

*University of Architecture & Civil Engr., 1 Hr. Smirnenski Blv.,
1421 Sofia, Bulgaria; E-mail: mmk_fte@uacg.acad.bg
**Dept. of Automatics, Technical University of Sofia, 1756 Sofia, Bulgaria
***Laboratoire d'Automatique de Grenoble, INPG-ENSIEG, BP 46,
38402 Saint-Martin-d'Heres Cedex, France



ABSTRACT



In this paper we study the sensitivity of the generalized Lyapunov equations (GLE) arising in the theory of linear descriptor systems. First, a local perturbation analysis of GLE is presented, which gives local linear and non-linear bounds for the perturbation in the solution as a function of the perturbations in the coefficient matrices. These bounds, however, are valid only asymptotically and their application for possibly small but nevertheless finite perturbations in the data requires additional justification. The disadvantage of the local bounds is overcome using the techniques of non-local perturbation analysis which is aimed at two things simultaneously: first to show that a solution of the perturbed equation exists, and second to find a non-local (and in general non-linear) perturbation bound for GLE. This bound is valid rigorously in contrast to the local bounds in which higher order terms are neglected. It is shown that the non-local bound obtained is asymptotically sharp, asymptotically exact or even exact in certain sense.



Keywords: Generalized Lyapunov equations, Perturbation analysis, Condition numbers

Date received: January 31, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeb-58.