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Robust \(H_{\infty}\) filtering for uncertain impulsive stochastic systems under sampled measurements. (English) Zbl 1012.93063
This paper is concerned with the problem of robust \(H_{\infty}\) filtering for uncertain impulsive stochastic systems under sampled measurements. The parameter uncertainties are assumed to be time-varying norm-bounded. The aim is to design a stochastically stable filter, using the locally sampled measurements, which ensures both the robust stochastic stability and a prescribed level of \(H_{\infty}\) performance for the filtering error dynamics for all admissible uncertainties. A sufficient condition for the existence of such a filter is proposed in terms of certain linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired filter is given. An example is provided to demonstrate the effectiveness of the proposed approach.

MSC:
93E11 Filtering in stochastic control theory
93B36 \(H^\infty\)-control
93C57 Sampled-data control/observation systems
93E15 Stochastic stability in control theory
93D09 Robust stability
34A37 Ordinary differential equations with impulses
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