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Abstract and Applied Analysis
Volume 2014, Article ID 867189, 7 pages
Research Article

Finite Time Stability of Stochastic Hybrid Systems

Department of Mathematics, Huizhou University, Huizhou 516007, China

Received 20 October 2013; Accepted 20 December 2013; Published 16 January 2014

Academic Editor: Ademir Fernando Pazoto

Copyright © 2014 Ying Yang and Guopei Chen. 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.


This paper considers the finite time stability of stochastic hybrid systems, which has both Markovian switching and impulsive effect. First, the concept of finite time stability is extended to stochastic hybrid systems. Then, by using common Lyapunov function and multiple Lyapunov functions theory, two sufficient conditions for finite time stability of stochastic hybrid systems are presented. Furthermore, a new notion called stochastic minimum dwell time is proposed and then, combining it with the method of multiple Lyapunov functions, a sufficient condition for finite time stability of stochastic hybrid systems is given. Finally, a numerical example is provided to illustrate the theoretical results.