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H ∞ Filtering for General Delayed Nonlinear Stochastic Systems with Markov Jumps

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Abstract

This paper is concerned with the robust \(H_{\infty }\) filtering problem of nonlinear stochastic delayed systems with Markov jumps, where time delay exists in state equation, measurement equation and controlled output. Firstly, by introducing a nonlinear stochastic bounded real lemma, we present the \(H_{\infty }\) filter design via solving a set of Hamilton-Jacobi inequalities (HJIs). Secondly, by using fuzzy approach, the \(H_{\infty }\) filter can be designed via solving a set of Linear Matrix inequalities instead of HJIs. Finally, two numerical examples are given to show the effectiveness of our results.

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Acknowledgements

This research was supported by NSF of China (Nos.61573227, 61633014), the Research Fund for the Taishan Scholar Project of Shandong Province of China, the SDUST Research Fund (No.2015TDJH105) and the State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources (No.LAPS16011).

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Authors and Affiliations

  1. College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, 266590, Shandong Province, China

    Weihai Zhang, Zhiteng Pan & Yan Li

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  1. Weihai Zhang
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  2. Zhiteng Pan
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  3. Yan Li
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Correspondence to Weihai Zhang.

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Zhang, W., Pan, Z. & Li, Y. H ∞ Filtering for General Delayed Nonlinear Stochastic Systems with Markov Jumps. Int. J. Fuzzy Syst. 19, 1989–2002 (2017). https://doi.org/10.1007/s40815-016-0288-4

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  • DOI: https://doi.org/10.1007/s40815-016-0288-4

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