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Stability and stabilization for uncertain fuzzy system with sampled-data control and state quantization

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Abstract

This paper studies the stability and stabilization problems of the T-S fuzzy systems with uncertainty and state quantization. Considering that fuzzy membership functions(FMFs) are the main characteristic of T-S fuzzy model, if the information about the membership function is not added, it will be conservative. So, a novel Lyapunov-Krasovskii functional (LKF) which contains not only integral variables but also FMFs is constructed. To include more information about the sampling pattern, the states on both sides of the sampling interval are incorporated into the LKF. When taking the derivative of the LKF, the product terms which consist of derivative of FMFs and LKF coefficient are involved. Then, the product terms are discussed to ensure their negative definition. By further derivation, enough stability conditions are expressed in the form of linear matrix inequalities (LMIs). The sampling intervals and controller parameters for the T-S fuzzy system can be solved by MATLAB toolbox with the optimal parameters. Finally, two numerical examples are simulated to illustrate the effectiveness of the proposed method.

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Acknowledgements

This work was funded by Natural Science Foundation-Steel and Iron Foundation of Hebei Province under Grant E2019105123, and Science and Technology Project of Hebei Education Department under Grant ZD2019311.

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Authors and Affiliations

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

    Liu Yang

  2. The Institute of Mining Engineering, North China University of Science and Technology, Hebei, Tangshan, 063009, China

    Jiayong Zhang

  3. The Institute of Electrical Engineering, North China University of Science and Technology, Hebei, Tangshan, 063009, China

    Chao Ge

  4. The Institute of Artificial Intelligence, North China University of Science and Technology, Hebei, Tangshan, 063009, China

    Wei Li

  5. Department of Computer Science and Technology, Tangshan University, Hebei, Tangshan, 063009, China

    Zhiwei Zhao

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  1. Liu Yang
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  2. Jiayong Zhang
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  3. Chao Ge
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  4. Wei Li
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  5. Zhiwei Zhao
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Correspondence to Jiayong Zhang, Chao Ge or Wei Li.

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Yang, L., Zhang, J., Ge, C. et al. Stability and stabilization for uncertain fuzzy system with sampled-data control and state quantization. Appl Intell 51, 7469–7483 (2021). https://doi.org/10.1007/s10489-021-02206-8

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