Abstract and Applied Analysis
Volume 2013 (2013), Article ID 548712, 8 pages
http://dx.doi.org/10.1155/2013/548712
Research Article

Exponential Stability of Impulsive Stochastic Functional Differential Systems with Delayed Impulses

Fengqi Yao,1 Feiqi Deng,2 and Pei Cheng3

1School of Electrical Engineering & Information, Anhui University of Technology, Ma'anshan, Anhui 243000, China
2The Institute of System Engineering, South China University of Technology, Guangzhou, Guangdong 510640, China
3School of Mathematical Science, Anhui University, Hefei, Anhui 230039, China

Received 6 December 2012; Revised 24 February 2013; Accepted 11 March 2013

Academic Editor: Cristina Pignotti

Copyright © 2013 Fengqi Yao et al. 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

A class of generalized impulsive stochastic functional differential systems with delayed impulses is considered. By employing piecewise continuous Lyapunov functions and the Razumikhin techniques, several criteria on the exponential stability and uniform stability in terms of two measures for the mentioned systems are obtained, which show that unstable stochastic functional differential systems may be stabilized by appropriate delayed impulses. Based on the stability results, delayed impulsive controllers which mean square exponentially stabilize linear stochastic delay systems are proposed. Finally, numerical examples are given to verify the effectiveness and advantages of our results.