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H ∞ Filtering for Stochastic Systems with Markovian Switching and Partly Unknown Transition Probabilities

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Abstract

This paper considers the H ∞ filtering problem for stochastic systems. The systems under consideration involve Markovian switching, mode-dependent delays, Itô-type stochastic disturbance, distributed time-varying delays and partly unknown transition probabilities. Our aim is to design a full-order filter such that the corresponding filtering error system is stochastically stable and satisfies a prescribed H ∞ disturbance attenuation level. By using a new Lyapunov–Krasovskii functional, sufficient conditions are formulated in terms of linear matrix inequalities (LMIs). A numerical example is given to illustrate the effectiveness of the proposed main results.

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Acknowledgements

This work was supported by the Fundamental Research Funds for the Central Universities (103.1.2E022050205), the Fund of Sichuan Provincial Key Laboratory of signal and information processing, Xihua University (SZJJ2009-002) and the National Basic Research Program of China (2010CB732501).

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Authors and Affiliations

  1. School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Yucai Ding, Hong Zhu, Yuping Zhang & Yong Zeng

  2. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Shouming Zhong

  3. Key Laboratory for Neuroinformation of Ministry of Education, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Shouming Zhong

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  1. Yucai Ding
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  2. Hong Zhu
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  3. Shouming Zhong
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  4. Yuping Zhang
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Correspondence to Yucai Ding.

Appendix: Proof of Lemma 1

Appendix: Proof of Lemma 1

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Ding, Y., Zhu, H., Zhong, S. et al. H ∞ Filtering for Stochastic Systems with Markovian Switching and Partly Unknown Transition Probabilities. Circuits Syst Signal Process 32, 559–583 (2013). https://doi.org/10.1007/s00034-012-9462-6

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