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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 401538, 9 pages
http://dx.doi.org/10.1155/2013/401538
Research Article

-Moment Stability of Stochastic Differential Delay Systems with Impulsive Jump and Markovian Switching

Department of Electrical Engineering and Automation, Qufu Normal University, Rizhao 276826, China

Received 2 February 2013; Revised 26 April 2013; Accepted 3 May 2013

Academic Editor: Yang Yi

Copyright © 2013 Lijun Gao. 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 investigates -moment stability of the stochastic differential delay systems with impulsive jump and Markovian switching. Some stability criteria are obtained based on Lyapunov functional method and stochastic theory. It is shown that, even if all the subsystems governing the continuous dynamics without impulse are not stable, as impulsive and switching signal satisfies a dwell-time upper bound condition, impulses can stabilize the systems in the -moment stability sense. The opposite situation is also developed for which all the subsystems governing the continuous dynamics are -moment stable. The results can be easily applied to stochastic systems with arbitrarily large delays. The efficiency of the proposed results is illustrated by two numerical examples.