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Mathematical Problems in Engineering
Volume 3, Issue 2, Pages 173-185
http://dx.doi.org/10.1155/S1024123X97000513

Stability of stochastic systems with jumps

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

Received 15 January 1996; Revised 30 April 1996

Copyright © 1996 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 stochastic stability of systems with Markovian jumps and Brownian motion. Mainly, we present sufficient conditions for quadratic stabilization of Ito type stochastic linear and nonlinear systems with Markovian jumps and Brownian motion using state feedback control. We also prove the guaranteed cost property of the proposed control strategy for the linear case.