Delay-Dependent Robust H∞ Filter Design for Uncertain Linear Systems with Time-Varying Delay

A new delay-dependent robust H∞ filtering design for uncertain linear systems with time-varying delay is investigated. Two kinds of time-varying delays are considered. One is differentiable uniformly bounded with a bounded delay derivative; the other is continuous uniformly bounded. A full-order filter is designed which ensures the asymptotic stability of the filtering error system and a prescribed level of H∞ performance for all possible parameters which reside in a given polytope. By constructing a new Lyapunov functional which contains a triple integral term, new delay-dependent conditions for the existence of the H∞ filter are derived which are less conservative than the existing ones. The filter gain can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, two numerical examples are given to show the effectiveness and the advantages of the proposed method.

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