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\({\mathscr {H}}_\infty\) Filtering of Stochastic Fuzzy Systems Based on Hybrid Modeling Technique with Aperiodic Sampled-Data

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Abstract

This paper is concerned with the problem of \({\mathscr {H}}_\infty\) fuzzy filtering for continuous nonlinear stochastic systems which can be approximated by the Takagi–Sugeno (T–S) fuzzy systems and the input is aperiodically sampled. We proposed the fuzzy parameters dependent filtering to estimate the state variables for nonlinear stochastic systems. In general, it is difficult to solve the filtering parameters under the hybrid modeling technique of the sampled-data. And the discrete feedback property under the input-delay technique of the sampled-data always disappears. Therefore, we introduce the improved hybrid modeling technique to keep the discrete feedback property of the closed-loop systems. Next, the improved time-varying Lyapunov function method is adopted to analyze the remodeled hybrid systems. Then the sufficient conditions of mean-squared exponential stability and \({\mathscr {H}}_\infty\) performance of the filtering error systems are obtained and the parameters of the fuzzy filtering can be solved. The proposed improved hybrid modeling technique can be widely applied to practically address the \({\mathscr {H}}_\infty\) filtering design problem. Finally, a practical example of the balancing problem about inverted pendulum is used to show the effectiveness of the theoretical results.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grants 62073144, 61573156, 61733008, 61873099, 61503142, the Natural Science Youth Development Foundation of South China Normal University Under Grants 20KJ14, the Natural Science Foundation of Guangdong Province under Grant 2020A1515-010441, and Guangzhou Science and Technology Planning Project Under Grants 202002030389, 202002030158

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Authors and Affiliations

  1. School of Computer Science, South China Normal University, Guangzhou, 510631, People’s Republic of China

    Shuqi Li & Jing Xiao

  2. Systems Engineering Institute, South China University of Technology, Guangzhou, 510640, People’s Republic of China

    Feiqi Deng

  3. School of Automation, Guangdong University of Technology, Guangzhou, 510006, People’s Republic of China

    Mali Xing

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  1. Shuqi Li
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  2. Feiqi Deng
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  3. Mali Xing
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  4. Jing Xiao
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Correspondence to Feiqi Deng.

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Li, S., Deng, F., Xing, M. et al. \({\mathscr {H}}_\infty\) Filtering of Stochastic Fuzzy Systems Based on Hybrid Modeling Technique with Aperiodic Sampled-Data. Int. J. Fuzzy Syst. 23, 2106–2117 (2021). https://doi.org/10.1007/s40815-021-01080-3

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  • DOI: https://doi.org/10.1007/s40815-021-01080-3

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