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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 93B36 ${H}^{\infty }$-control 93C10 Nonlinear control systems