Stochastic stability of semi-Markovian jump systems with mode-dependent delays

• Published in: International journal of robust and nonlinear control Vol. 24; no. 18; pp. 3317 - 3330
• Main Authors: Li, Fanbiao, Wu, Ligang, Shi, Peng
• Format: Journal Article
• Language: English
• Published: Bognor Regis Blackwell Publishing Ltd 01.12.2014; Wiley Subscription Services, Inc
• Subjects: Delay; Dynamical systems; Lyapunov functions; Markov processes; mode-dependent time-delays; Nonlinear dynamics; semi-Markovian jump systems; Stability; Stochastic processes; stochastic stability; Stochasticity
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.3057

SUMMARYSemi‐Markovian jump systems, due to the relaxed conditions on the stochastic process, and its transition rates are time varying, can be used to describe a larger class of dynamical systems than conventional full Markovian jump systems. In this paper, the problem of stochastic stability for a class of semi‐Markovian systems with mode‐dependent time‐variant delays is investigated. By Lyapunov function approach, together with a piecewise analysis method, a sufficient condition is proposed to guarantee the stochastic stability of the underlying systems. As more time‐delay information is used, our results are much less conservative than some existing ones in literature. Finally, two examples are given to show the effectiveness and advantages of the proposed techniques. Copyright © 2013 John Wiley & Sons, Ltd.