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Stochastic stability of semi‐Markovian jump systems with mode‐dependent delays
Author(s) -
Li Fanbiao,
Wu Ligang,
Shi Peng
Publication year - 2014
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3057
Subject(s) - piecewise , stability (learning theory) , markov process , jump , class (philosophy) , control theory (sociology) , lyapunov function , computer science , mode (computer interface) , function (biology) , jump process , mathematics , mathematical optimization , control (management) , nonlinear system , mathematical analysis , physics , statistics , quantum mechanics , machine learning , artificial intelligence , operating system , evolutionary biology , biology
SUMMARY Semi‐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.