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Stability and Stabilization of Delayed Fuzzy Semi-Markov Jump Systems with Incomplete Transition Rates and Quadratic Fuzzy Lyapunov Matrix via Quantized Control Design

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Abstract

This study examines the stability and stabilization issues of a type of state-quantized, time-varying delayed (TVD) Takagi–Sugeno (T–S) fuzzy semi-Markov jump systems. First of all, in order to obtain more information of T–S fuzzy systems, an augmented fuzzy Lyapunov–Krasovskii Functional (LKF) is formatted including a quadratic fuzzy Lyapunov matrix (QFLM). In addition, a novel quadratic polynomial inequality (QPI) is applied to narrow the estimation gap for TVD and a quantized controller is used to reduce control accuracy. Then, the sufficient conditions for system stability and stabilization via quantized controller are attained on the basis of Lyapunov stability theory and linear matrix inequalities method. Finally, three examples show how the constructed controller can successfully regulate the examined system and the proposed technique is less conservative than those of the former ones.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grants 12061088, the Basic Research Youth Fund Project of Yunnan Science and Technology Department under Grant 202201AU070046, and the Scientific Research Fund Project of Yunnan Provincial Department of Education under Grant 2022J0447.

Author information

Authors and Affiliations

  1. School of Mathematics and Computer Science, Yunnan Minzu University, Kunming, 650500, China

    Jiangping Zhang & Haiyang Zhang

  2. School of Media and Information Engineering, Yunnan Open University, Kunming, 650504, China

    Lianglin Xiong

  3. Department of Mathematics, Yunnan University, Kunming, 650091, China

    Yongkun Li

  4. School of Mathematics, Southeast University, Nanjing, 211189, China

    Jinde Cao

  5. The School of Computer Science, Sichuan University, Chengdu, 610065, China

    Yi Zhang

  6. Ahlia University, Manama , 10878, Bahrain

    Jinde Cao

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  1. Jiangping Zhang
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  2. Lianglin Xiong
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Correspondence to Lianglin Xiong.

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Zhang, J., Xiong, L., Zhang, H. et al. Stability and Stabilization of Delayed Fuzzy Semi-Markov Jump Systems with Incomplete Transition Rates and Quadratic Fuzzy Lyapunov Matrix via Quantized Control Design. Int. J. Fuzzy Syst. 26, 2300–2322 (2024). https://doi.org/10.1007/s40815-024-01736-w

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  • DOI: https://doi.org/10.1007/s40815-024-01736-w

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