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Exponential \(H_{\infty }\) filtering for time-varying delay systems: Markovian approach. (English) Zbl 1217.93170
Summary: This paper discusses the \(H_{\infty }\) filtering problem for a class of deterministic systems with time-varying delays, where the stochastic property of time-varying delays described by Markovian approach is taken into consideration in filter design. Firstly, the delay interval is separated into several subintervals, which can be described by Markov process. Then, a new \(H_{\infty }\) filtering method for deterministic system with time-varying delay is given, whose filter can switch with time delay in terms of Markov process. Sufficient conditions for the existence of \(H_{\infty }\) filter are obtained as linear matrix inequalities, where the mode transition rates are known exactly or inexactly. Finally, numerical examples are used to demonstrate the utility of the given methods.

MSC:
93E11 Filtering in stochastic control theory
93B36 \(H^\infty\)-control
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