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Exponential H ∞  filtering for stochastic Markovian jump systems with time delays

Authors

  • Yun Chen,

    1. Institute of Information and Control, Hangzhou Dianzi University, Hangzhou 310018, China
    2. School of Computing, Engineering and Mathematics, University of Western Sydney, Penrith NSW 2751, Australia
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  • Wei Xing Zheng

    Corresponding author
    1. School of Computing, Engineering and Mathematics, University of Western Sydney, Penrith NSW 2751, Australia
    • Correspondence to: Wei Xing Zheng, School of Computing, Engineering and Mathematics, University of Western Sydney, Penrith NSW 2751, Australia.

      E-mail: w.zheng@uws.edu.au

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SUMMARY

This paper investigates the problem of exponential H ∞  filtering for stochastic systems with time delays and Markovian jumping parameters. On the basis of Lyapunov–Krasovskii functional theory and generalized Finsler lemma, a delay-dependent bounded real lemma is established without using any model transformations, bounding techniques for cross terms, or additional free matrix variables. The obtained bounded real lemma guarantees that the filtering error system is both mean-square exponentially stable and almost surely exponentially stable with a prescribed H ∞  noise attenuation level. Then an exponential H ∞  filter is designed for stochastic retarded Markovian jump systems in terms of a set of LMIs. Meanwhile, the mathematical equivalence of the proposed method to one recent method is presented, but our proposed method is more computationally efficient with fewer matrix variables than that recent method. The validity of the method is verified by a numerical example.Copyright © 2012 John Wiley & Sons, Ltd.

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