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Stochastic Switched Sampled-Data Control for Uncertain Fuzzy Systems with Packet Dropout

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Abstract

This paper addresses the stability and stabilization problems of uncertain Takagi–Sugeno (T-S) fuzzy system with control packet dropout. The process of packet loss is proposed, which is modeled according to some white noise sequences of Bernoulli distribution. Then, under the zero-input strategy, a newly stochastic switched sampled-data controller is introduced. Based on the Lyapunov function method, a novel Lyapunov–Krasovskii (LKF) function is constructed via introducing a fuzzy membership functions (FMFs), which can use the information about the actual sampling pattern. Each term of the LKF need not be positive, but it needs to be positive at sampling instants. Using the reciprocally convex method and relaxed free-matrix-based (FMB) integral inequality, novel stabilization criteria are established to guarantee that the T-S fuzzy system is stochastic stable when the control packet dropout occurs in a random way. Based on the linear matrix inequalities (LMIs), a fuzzy controller design algorithm for sampled data is presented to obtain a larger sampling interval. Finally, two numerical examples are used to verify the effectiveness and advantages of the proposed method.

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Acknowledgements

This paper is partially supported by the National Key Research and Development Plan (2018YFC0808104), the National Natural Science Foundation Fund (51874012), the Hebei Natural Science Foundation Fund (E2020209074), the Hebei Natural Science Foundation–Steel and Iron Foundation Fund (E2019105123), the Hebei Education Department Foundation Fund (ZD2019311).

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Authors and Affiliations

  1. Institute of Electrical Engineering, North China University of Science and Technology, Tangshan, 063009, China

    Chao Ge & Liu Yang

  2. Department of Computer Engineering, Tangshan College, Tangshan, 063009, China

    Zhiwei Zhao

  3. Institute of Mining Engineering, North China University of Science and Technology, Tangshan, 063009, China

    Jiayong Zhang

  4. School of Control and Computer Engineering, North China Electric Power University, Beijing, 102206, China

    Yajuan Liu

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  1. Chao Ge
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  2. Liu Yang
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  4. Jiayong Zhang
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Correspondence to Chao Ge or Jiayong Zhang.

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Ge, C., Yang, L., Zhao, Z. et al. Stochastic Switched Sampled-Data Control for Uncertain Fuzzy Systems with Packet Dropout. Int. J. Fuzzy Syst. 23, 145–157 (2021). https://doi.org/10.1007/s40815-020-00992-w

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  • DOI: https://doi.org/10.1007/s40815-020-00992-w

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