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Image control for discrete-time singularly perturbed systems with two Markov processes. (English) Zbl 1286.93194
Summary: This paper discusses the \(H_{\infty}\) state feedback control problem for discrete-time Markovian jump singularly perturbed systems whose singularly perturbation parameters belong to another Markov process. Firstly, new mean-square exponential stability condition with \(H_{\infty}\) performance for discrete-time singularly perturbed systems with two Markov processes is given in terms of linear matrix inequalities (LMIs) with equality constraints via a novel method. Then, based on the derived stability condition where \(\varepsilon\) is involved, however, an \(H_{\infty}\) controller which is independent of \(\varepsilon\) is constructed. An effective iterative algorithm involving linear matrix inequalities is suggested to solve the matrix inequalities characterizing the \(H_{\infty}\) controller solutions. Finally, illustrative examples are presented to show the benefits and validity of the proposed approaches.

MSC:
93E15 Stochastic stability in control theory
93B36 \(H^\infty\)-control
93C70 Time-scale analysis and singular perturbations in control/observation systems
93C55 Discrete-time control/observation systems
60J75 Jump processes (MSC2010)
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