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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 524584, 6 pages
http://dx.doi.org/10.1155/2015/524584
Research Article

Further Results on Stability Analysis of Discrete-Time Markov Jump Linear Systems with Time-Varying Delay and Partly Known Transition Probabilities

State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China

Received 8 August 2014; Revised 23 October 2014; Accepted 23 October 2014

Academic Editor: Quanxin Zhu

Copyright © 2015 Xingang Zhao 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

This paper is concerned with the stability analysis of discrete-time Markov jump linear systems (MJLSs) with time-varying delay and partly known transition probabilities. The time delay is varying between lower and upper bounds, and the partly known transition probabilities cover the cases of known, uncertain with known lower and upper bounds, and completely unknown, which is more general than the existing result. Via constructing an appropriate Lyapunov function and employing a new technique to separate Lyapunov variables from unknown transition probabilities, a novel stability criterion is obtained in the framework of linear matrix inequality. A numerical example is given to show the effectiveness of the proposed approach.