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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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