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\(H_{\infty }\) filtering on nonlinear stochastic systems with delay. (English) Zbl 1136.93044
Summary: This paper is concerned with the problem of \(H_{\infty }\) filtering for a class of nonlinear Itô stochastic systems with delay. The objective is to design such a full-order filter that the \(L_{2}\) gain from the exogenous input to an estimation error is minimized or guaranteed to be less or equal to a prescribed value. Sufficient conditions are obtained for the existence of desired \(H_{\infty }\) filters, which are given in terms of the solutions to quadratic matrix inequalities involving scalar parameters. A numerical example is provided to demonstrate the effectiveness of the proposed approach.

MSC:
93E11 Filtering in stochastic control theory
93B36 \(H^\infty\)-control
93C10 Nonlinear systems in control theory
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