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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 191458, 9 pages
http://dx.doi.org/10.1155/2015/191458
Research Article

Stochastic Stability of Discrete-Time Switched Systems with a Random Switching Signal

1School of Mathematics and Statistics, Zhengzhou University, China
2College of Science, Henan Institute of Engineering, Zhengzhou, China

Received 13 December 2014; Revised 15 April 2015; Accepted 4 May 2015

Academic Editor: Alexander Klimenko

Copyright © 2015 Kai Liu 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.

Abstract

Necessary and sufficient condition for stochastic stability of discrete-time linear switched system with a random switching signal is considered in this paper, assuming that the switching signal allows fixed dwell time before a Markov switch occurs. It is shown that the stochastic stability of the system is equivalent to that of an auxiliary system with state transformations at switching time, whose switching signal is a Markov chain. The stochastic stability is studied using a stochastic Lyapunov approach. The effectiveness of the proposed approach is demonstrated by a numerical example.