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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 623014, 12 pages
http://dx.doi.org/10.1155/2012/623014
Research Article

Mean Square Exponential Stability of Stochastic Switched System with Interval Time-Varying Delays

Faculty of Science, Maejo University, Chiangmai 50290, Thailand

Received 19 March 2012; Revised 5 May 2012; Accepted 9 May 2012

Academic Editor: Miroslava Růžičková

Copyright © 2012 Manlika Rajchakit and Grienggrai Rajchakit. 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 is concerned with mean square exponential stability of switched stochastic system with interval time-varying delays. The time delay is any continuous function belonging to a given interval, but not necessary to be differentiable. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, a switching rule for the mean square exponential stability of switched stochastic system with interval time-varying delays and new delay-dependent sufficient conditions for the mean square exponential stability of the switched stochastic system are first established in terms of LMIs. Numerical example is given to show the effectiveness of the obtained result.