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