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Local H ∞ Control for Continuous-Time T-S Fuzzy Systems via Generalized Non-Quadratic Lyapunov Functions

Author

Listed:
  • Guolin Hu

    (School of Information and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China)

  • Jian Zhang

    (School of Information and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China)

  • Zhiguo Yan

    (School of Information and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China)

Abstract

This paper further develops a relaxed method to reduce conservatism in H ∞ feedback control for continuous-time T-S fuzzy systems via a generalized non-quadratic Lyapunov function. Different from the results of some exisiting works, the generalized H ∞ state feedback controller is designed. The relaxed stabilization conditions are obtained by applying Finsler’s lemma with the homogenous polynomial multipliers, and the H ∞ performance is acquired by solving an optimization problem. In addition, the proposed method could be expanded to handle other control problems for fuzzy systems. Two examples are given to show the validity of the proposed results.

Suggested Citation

  • Guolin Hu & Jian Zhang & Zhiguo Yan, 2022. "Local H ∞ Control for Continuous-Time T-S Fuzzy Systems via Generalized Non-Quadratic Lyapunov Functions," Mathematics, MDPI, vol. 10(19), pages 1-13, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3438-:d:921447
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    References listed on IDEAS

    as
    1. Flávio Faria & Geraldo Silva & Vilma Oliveira, 2013. "Reducing the conservatism of LMI-based stabilisation conditions for TS fuzzy systems using fuzzy Lyapunov functions," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(10), pages 1956-1969.
    2. Xiao-Heng Chang & Guang-Hong Yang & Haibo Wang, 2011. "Observer-based -control for discrete-time T–S fuzzy systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(10), pages 1801-1809.
    3. Hakim Achour & Djamel Boukhetala & Hilal Labdelaoui, 2020. "An observer-based robust H∞ controller design for uncertain Takagi–Sugeno fuzzy systems with unknown premise variables using particle swarm optimisation," International Journal of Systems Science, Taylor & Francis Journals, vol. 51(14), pages 2563-2581, October.
    4. Yan, Zhiguo & Zhang, Min & Chang, Gaizhen & Lv, Hui & Park, Ju H., 2022. "Finite-time annular domain stability and stabilization of Itô stochastic systems with Wiener noise and Poisson jumps-differential Gronwall inequality approach," Applied Mathematics and Computation, Elsevier, vol. 412(C).
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