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Stability and stabilization of discrete-time singular Markov jump systems with time-varying delay. (English) Zbl 1185.93144
Summary: The stochastic stability and stochastic stabilization of time-varying delay discrete-time singular Markov jump systems are discussed. For full and partial knowledge of transition probabilities cases, delay-dependent Linear Matrix Inequalities (LMIs) conditions for the systems to be regular, causal and stochastically stable are derived. Sufficient conditions are proposed for the existence of state feedback controller in terms of LMIs. Finally, two numerical examples are given to illustrate the effectiveness of the method.

MSC:
93E15 Stochastic stability in control theory
60J75 Jump processes (MSC2010)
93C55 Discrete-time control/observation systems
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