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Weighted \(\mathcal H _{\infty}\) filtering of switched systems with time-varying delay: average dwell time approach. (English) Zbl 1191.94053

Summary: This paper is concerned with the \(\mathcal H _{\infty }\) filtering problem for a continuous-time linear switched system with time-varying delay in its state. To reduce the overdesign of the quadratic framework, this paper proposes a parameter-dependent filter design procedure, which is much less conservative than the quadratic approach. By using an average dwell time approach and the piecewise Lyapunov function technique, a sufficient condition is first proposed to guarantee the exponential stability with a weighted \(\mathcal H _{\infty }\) performance for the filtering error system with the decay estimate explicitly given. Then, the corresponding solvability condition for a desired filter is established, and the filter design is cast into a convex optimization problem which can be efficiently handled by using standard numerical software. All the conditions obtained in this paper are delay dependent. Finally, a numerical example is given to illustrate the effectiveness of the proposed theory.

MSC:

94A12 Signal theory (characterization, reconstruction, filtering, etc.)
93B36 \(H^\infty\)-control
93E11 Filtering in stochastic control theory
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