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Robust output feedback \(H_{}\) control of uncertain Markovian jump systems with mode-dependent time-delays. (English) Zbl 1194.93181
Summary: This paper describes the synthesis of robust output feedback \(H_{\infty }\) control for a class of uncertain Markovian jump linear systems with time-delays which are time-varying and depend on the system modes of operation. Under the assumption of known bounds of system uncertainties and the control system gain variations, we present sufficient conditions on the existence of robust stochastic stability and \(\gamma \)-disturbance \(H_{\infty }\) attenuation. Through the changes of variables and Schur complements, these sufficient conditions can be rewritten in a set of coupled linear matrix inequalities, with which, robust control can be easily constructed. As an added advantage, the control design depends only on \(p^o_{mj,t}\), the measured parameter of Markovian jumping at time \(t\), which might be corrupted by measurement noises. Numerical examples are provided to demonstrate the effectiveness of the proposed approach.

MSC:
93D15 Stabilization of systems by feedback
15A39 Linear inequalities of matrices
93B35 Sensitivity (robustness)
93B36 \(H^\infty\)-control
93E03 Stochastic systems in control theory (general)
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