Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 296136, 15 pages
http://dx.doi.org/10.1155/2012/296136
Research Article

Exponential Stability of Impulsive Stochastic Delay Differential Systems

Xiaotai Wu,1,2 Litan Yan,1 Wenbing Zhang,3 and Liang Chen3

1Department of Mathematics, Donghua University, Shanghai 201620, China
2Department of Mathematics, Anhui Polytechnic University, Wuhu, Anhui 241000, China
3School of Information Science and Technology, Donghua University, Shanghai 201620, China

Received 13 July 2011; Accepted 5 October 2011

Academic Editor: Garyfalos Papaschinopoulos

Copyright © 2012 Xiaotai Wu 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

This paper investigates the stability of stochastic delay differential systems with two kinds of impulses, that is, destabilizing impulses and stabilizing impulses. Both the 𝑝 th moment and almost sure exponential stability criteria are established by using the average impulsive interval. When the impulses are regarded as disturbances, a lower bound of average impulsive interval is obtained; it means that the impulses should not happen too frequently. On the other hand, when the impulses are used to stabilize the system, an upper bound of average impulsive interval is derived; namely, enough impulses are needed to stabilize the system. The effectiveness of the proposed results is illustrated by two examples.