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Quantized \(H_{\infty }\) Filtering for Continuous-Time Nonhomogeneous Markov Jump Systems

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Abstract

This paper investigates the problems of quantized \(H_{\infty }\) filtering for continuous-time nonhomogeneous Markov jump systems. The transition probability matrix is assumed to be time-varying and lies in a convex bounded domain. Firstly, we design the \(H_{\infty }\) filter with a mode-dependent logarithmic quantizer. Then based on the mode-dependent and parameter-dependent Lyapunov function, the stochastic stability with a prescribed \(H_{\infty }\) performance index is guaranteed by fully considering the information of time-varying transition probability. Specifically, stability criteria are established to make system stochastically stable and a cost function is given to satisfy the \(H_{\infty }\) performance. Finally, both numerical examples and practical example are given to illustrate the less conservatism and the feasibility of the proposed quantized filer design methods.

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Acknowledgements

The authors thank the editor and the reviewers for their constructive comments and suggestions to improve the manuscript. This work was supported by the Natural Science Foundation of Jiangsu Province under Grant BK20181157, the Fundamental Research Funds for the Central Universities under Grant 2019B22114 and Qing Lan Project (Grant Szx/16A205).

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Correspondence to Mingang Hua.

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Hua, M., Bian, C., Chen, J. et al. Quantized \(H_{\infty }\) Filtering for Continuous-Time Nonhomogeneous Markov Jump Systems. Circuits Syst Signal Process (2020). https://doi.org/10.1007/s00034-020-01343-8

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Keywords

  • \(H_{\infty }\) filtering
  • Markov jump systems
  • Time-varying
  • Mode-dependent logarithmic quantizer
  • Lyapunov function