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Robust \(\mathcal H_{\infty}\) control of descriptor discrete-time Markovian jump systems. (English) Zbl 1120.93057
Summary: This paper considers the stochastic stability and the robust \(\mathcal H_{\infty}\) control of descriptor discrete-time systems with Markovian jumping parameters. In terms of linear matrix inequalities, a necessary and sufficient condition is proposed, which ensures a discrete-time descriptor Markovian jump system to be regular, causal and stochastically stable. A robust admissibility condition and a robust bounded real lemma are also developed. Based on these, a sufficient condition on the existence of a state-feedback controller which guarantees the robust admissibility and the \(\mathcal H_{\infty}\) performance is also given by employing the linear matrix inequality technique. A robustly stabilizing \(\mathcal H_{\infty}\) state feedback controller can be constructed through the numerical solutions of linear matrix inequalities. Finally, an example is provided to demonstrate the effectiveness of the proposed approach.

93E20 Optimal stochastic control
93E03 Stochastic systems in control theory (general)
93C55 Discrete-time control/observation systems
93B35 Sensitivity (robustness)
93E15 Stochastic stability in control theory
93D21 Adaptive or robust stabilization
93B50 Synthesis problems
Full Text: DOI
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