## $$H_{\infty }$$ 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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### References:

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