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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 |

### Keywords:

exponential stability; linear matrix inequality (LMI); switched systems; time-varying delay; \(\mathcal H _{\infty }\) filtering
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\textit{L. Wu} and \textit{J. Lam}, Circuits Syst. Signal Process. 28, No. 6, 1017--1036 (2009; Zbl 1191.94053)

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