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Weighted H ∞ Filtering of Switched Systems with Time-Varying Delay: Average Dwell Time Approach

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Abstract

This paper is concerned with the H ∞ 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 H ∞ 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.

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Authors and Affiliations

  1. Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin, 150001, P.R. China

    Ligang Wu

  2. Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, Hong Kong

    James Lam

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  1. Ligang Wu
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  2. James Lam
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Correspondence to Ligang Wu.

Additional information

This work was supported in part by the National Natural Science Foundation of China under Grants 60804002 and 60834003, 973 Project (2009CB320600), and in part by a research grant from RGC HKU 7029/05P.

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Wu, L., Lam, J. Weighted H ∞ Filtering of Switched Systems with Time-Varying Delay: Average Dwell Time Approach. Circuits Syst Signal Process 28, 1017–1036 (2009). https://doi.org/10.1007/s00034-009-9123-6

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  • DOI: https://doi.org/10.1007/s00034-009-9123-6

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