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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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