Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 176375, 16 pages
http://dx.doi.org/10.1155/2012/176375
Research Article

Stability and Stabilization of Impulsive Stochastic Delay Differential Equations

Kaining Wu and Xiaohua Ding

Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, China

Received 6 February 2012; Revised 27 March 2012; Accepted 27 March 2012

Academic Editor: Zhijian Ji

Copyright © 2012 Kaining Wu and Xiaohua Ding. 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

We consider the stability and stabilization of impulsive stochastic delay differential equations (ISDDEs). Using the Lyapunov-Razumikhin method, we obtain the sufficient conditions to guarantee the pth moment exponential stability of ISDDEs. Then the almost sure exponential stability is considered and the sufficient conditions of the almost sure exponential stability are obtained. Moreover, the stabilization problem of ISDDEs is studied and the criterion on impulsive stabilization of ISDDEs is established. At last, examples are presented to illustrate the correctness of our results.