## 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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### References:

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