Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 592036, 15 pages
Research Article

Stability and Stabilization of Impulsive Stochastic Delay Difference Equations

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

Received 7 December 2009; Accepted 16 January 2010

Academic Editor: Leonid Shaikhet

Copyright © 2010 Kaining 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.


When an impulsive control is adopted for a stochastic delay difference system (SDDS), there are at least two situations that should be contemplated. If the SDDS is stable, then what kind of impulse can the original system tolerate to keep stable? If the SDDS is unstable, then what kind of impulsive strategy should be taken to make the system stable? Using the Lyapunov-Razumikhin technique, we establish criteria for the stability of impulsive stochastic delay difference equations and these criteria answer those questions. As for applications, we consider a kind of impulsive stochastic delay difference equation and present some corollaries to our main results.