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Stochastic stability and stabilization of discrete‐time singular Markovian jump systems with partially unknown transition probabilities
Author(s) -
Wang Jianhua,
Zhang Qingling,
Yan XingGang,
Zhai Ding
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.3146
Subject(s) - stability (learning theory) , control theory (sociology) , set (abstract data type) , jump , markov process , discrete time and continuous time , mathematics , controller (irrigation) , state (computer science) , computer science , control (management) , algorithm , physics , statistics , quantum mechanics , artificial intelligence , machine learning , agronomy , biology , programming language
Summary This paper considers the stochastic stability and stabilization of discrete‐time singular Markovian jump systems with partially unknown transition probabilities. Firstly, a set of necessary and sufficient conditions for the stochastic stability is proposed in terms of LMIs, then a set of sufficient conditions is proposed for the design of a state feedback controller to guarantee that the corresponding closed‐loop systems are regular, causal, and stochastically stable by employing the LMI technique. Finally, some examples are provided to demonstrate the effectiveness of the proposed approaches. Copyright © 2014 John Wiley & Sons, Ltd.