## A new approach to robust $$\mathcal H_{\infty }$$ filtering for uncertain systems with both discrete and distributed delays.(English)Zbl 1118.93024

Summary: This paper is concerned with robust $$H_{\infty }$$ filter design for a class of linear distributed delay systems with norm-bounded time-varying parameter uncertainties. The distributed delays are assumed to appear in both state and measurement equations. A new design method is proposed by introducing some relaxation matrices and tuning parameters, which can be chosen properly to lead to a less conservative result. A sufficient condition is obtained to guarantee the existence of desired $$H_{\infty }$$ filters, which can be constructed by solving a convex optimization problem. A numerical example is included to illustrate the effectiveness and the reduced conservatism of the proposed design technique.

### MSC:

 93B36 $$H^\infty$$-control 93C41 Control/observation systems with incomplete information 93C15 Control/observation systems governed by ordinary differential equations 93C05 Linear systems in control theory 93D09 Robust stability
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