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Mathematical Problems in Engineering
Volume 3, Issue 3, Pages 187-201
http://dx.doi.org/10.1155/S1024123X97000525

Stochastic stability of linear time-delay system with Markovian jumping parameters

Mechanical Engineering Department, École Polytechnique de Montréal, P.O. Box 6079, Station “centre-ville”, Montréal H3C 3A7, Québec, Canada

Received 12 February 1996; Revised 30 April 1996

Copyright © 1997 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper deals with the class of linear time-delay systems with Markovian jumping parameters (LTDSMJP). We mainly extend the stability results of the deterministic class of linear systems with time-delay to this class of systems. A delay-independent necessary condition and sufficient conditions for checking the stochastic stability are established. A sufficient condition is also given. Some numerical examples are provided to show the usefulness of the proposed theoretical results.