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\(\mathcal{H}_{\infty}\) Filtering for Short-Time Switched Discrete-Time Linear Systems

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Abstract

In this paper, the \(\mathcal{H}_{\infty}\) filtering problem for a class of short-time switched discrete-time linear systems is investigated. For such systems, switching always occurs in some short interval. Since the error state may attain large unacceptable values in short-time switching intervals, besides the asymptotic stability of error dynamics, the boundedness of error state is also significant for short-time switched systems. Thus the designed filter is composed of two parts: asymptotic filter, based upon the existing results, ensures the asymptotic stability of the system during normal, relatively long interval, and finite-time filter ensures system to be finite-time bounded during the short interval of switching, which is the main concern in this paper. By introducing the concept of finite-time boundedness, the proposed filter is formulated as a set of sub-filters ensuring the error dynamics \(\mathcal{H}_{\infty}\) finite-time bounded in the short switching interval. Finally, a numerical example is provided to illustrate the effectiveness of this approach.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Nos. 51177137, 61134001). The authors would like to thank the associate editor and the reviewers for their helpful comments and suggestions which have helped improve the presentation of the paper.

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Authors and Affiliations

  1. School of Electrical Engineering, Southwest Jiaotong University, No. 111, Erhuanlu Beiyiduan, Chengdu, 610031, P.R. China

    Weiming Xiang, Jian Xiao & Muhammad Naveed Iqbal

  2. School of Applied Technology, Southwest University of Science and Technology, Mianyang, 621000, China

    Weiming Xiang

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  1. Weiming Xiang
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  2. Jian Xiao
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  3. Muhammad Naveed Iqbal
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Correspondence to Weiming Xiang.

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Xiang, W., Xiao, J. & Iqbal, M.N. \(\mathcal{H}_{\infty}\) Filtering for Short-Time Switched Discrete-Time Linear Systems. Circuits Syst Signal Process 31, 1927–1949 (2012). https://doi.org/10.1007/s00034-012-9416-z

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  • DOI: https://doi.org/10.1007/s00034-012-9416-z

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