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Robust H∞ stabilization for T-S fuzzy systems with time-varying delays and memory sampled-data control

Author

Listed:
  • Ge, Chao
  • Shi, Yanpen
  • Park, Ju H.
  • Hua, Changchun

Abstract

In this paper, we address the robust H∞ stabilization for T-S fuzzy systems with time-varying delays based on memory sampled-data control. By developing some new terms, an improved piecewise Lyapunov–Krasovskii functional (LKF) is constructed to take full advantage of characteristic about real sampling pattern. Furthermore, some relaxed matrices proposed in the LKF are not necessarily positive definite. By using the LKF and Free-Matrix-Based (FMB) integral inequality, some sufficient criteria are established to ensure the stability of fuzzy systems and reduce the influence of external disturbance with an H∞ norm bound. Then, the memory sampled-data controller can be derived by solving a group of linear matrix inequalities (LMIs) with the maximal sampling period. Finally, a numerical example is given to demonstrate the benefits and the superiority of the approach proposed.

Suggested Citation

  • Ge, Chao & Shi, Yanpen & Park, Ju H. & Hua, Changchun, 2019. "Robust H∞ stabilization for T-S fuzzy systems with time-varying delays and memory sampled-data control," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 500-512.
    • Handle: RePEc:eee:apmaco:v:346:y:2019:i:c:p:500-512
    DOI: 10.1016/j.amc.2018.10.076
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    References listed on IDEAS

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    1. Wang, Jing & Liang, Kun & Huang, Xia & Wang, Zhen & Shen, Hao, 2018. "Dissipative fault-tolerant control for nonlinear singular perturbed systems with Markov jumping parameters based on slow state feedback," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 247-262.
    2. Zhang, Ruimei & Zeng, Deqiang & Zhong, Shouming & Yu, Yongbin, 2017. "Event-triggered sampling control for stability and stabilization of memristive neural networks with communication delays," Applied Mathematics and Computation, Elsevier, vol. 310(C), pages 57-74.
    3. Li, Min & Shu, Feng & Liu, Duyu & Zhong, Shouming, 2018. "Robust H∞ control of T-S fuzzy systems with input time-varying delays: A delay partitioning method," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 209-222.
    4. Zeng, Deqiang & Zhang, Ruimei & Liu, Yajuan & Zhong, Shouming, 2017. "Sampled-data synchronization of chaotic Lur’e systems via input-delay-dependent-free-matrix zero equality approach," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 34-46.
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    Cited by:

    1. Sakthivel, R. & Suveetha, V.T. & Nithya, V. & Sakthivel, R., 2021. "Finite-time reliable filtering for Takagi–Sugeno fuzzy semi-Markovian jump systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 403-418.
    2. Ye, Dan & Li, Xiehuan, 2020. "Event-triggered fault detection for continuous-time networked polynomial-fuzzy-model-based systems," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    3. Gao, Meng & Zhang, Lihua & Qi, Wenhai & Cao, Jinde & Cheng, Jun & Kao, Yonggui & Wei, Yunliang & Yan, Xiaoyu, 2020. "SMC for semi-Markov jump T-S fuzzy systems with time delay," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    4. Jia, Jinping & Dai, Hao & Li, Li & Zhang, Fandi, 2021. "Global sampled-data stabilization for a class of nonlinear systems with arbitrarily long input delays via a multi-rate control algorithm," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    5. de Oliveira, Fúlvia S.S. & Souza, Fernando O., 2020. "Further refinements in stability conditions for time-varying delay systems," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    6. Luo, Jinnan & Liu, Xinzhi & Tian, Wenhong & Zhong, Shouming & Shi, Kaibo & Cheng, Jun, 2020. "A new approach to generalized dissipativity analysis for fuzzy systems with coupling memory sampled-data control," Applied Mathematics and Computation, Elsevier, vol. 368(C).

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