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Convergence criteria of fuzzy bilinear systems subject to bounded uncertainties

Author

Listed:
  • Hadj Taieb Nizar

    (University of Sfax, IPEIS)

  • Hammami Mohamed Ali

    (University of Sfax, Faculty of Sciences of Sfax)

  • Delmotte François

    (University of Artois)

Abstract

An effective method for examining stability and resolving different fuzzy controller design issues for Takagi–Sugeno (T–S) fuzzy systems, which encompass a broad category of nonlinear systems, is the linear matrix inequality approach. Moreover, the Lyapunov method is a very effective tool for studying the stability of this class of fuzzy systems. This paper explores the potential applications of these approaches for a class of perturbed fuzzy systems where the stability is considered for the nominal system, which is assumed to be bilinear with specific constraints on the uncertainties. We construct a fuzzy controller that guarantees the ultimate boundedness of the solutions of the uncertain bilinear Takagi–Sugeno fuzzy systems in order to study the convergence of solutions of the closed-loop system even in cases where the origin is not the equilibrium point of the system. One of the advantages of the method used in this work is the possibility of studying the convergence of trajectories towards a particular neighborhood of the origin which characterizes the asymptotic behavior of the system where a rate of convergence can be estimated. Furthermore, we show that the Van de Vusse reactor model illustrates the validity of the main result.

Suggested Citation

  • Hadj Taieb Nizar & Hammami Mohamed Ali & Delmotte François, 2025. "Convergence criteria of fuzzy bilinear systems subject to bounded uncertainties," Fuzzy Optimization and Decision Making, Springer, vol. 24(2), pages 197-222, June.
    • Handle: RePEc:spr:fuzodm:v:24:y:2025:i:2:d:10.1007_s10700-025-09443-3
    DOI: 10.1007/s10700-025-09443-3
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    References listed on IDEAS

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    1. A. Javier Barragán & Juan M. Enrique & Antonio J. Calderón & José M. Andújar, 2018. "Discovering the dynamic behavior of unknown systems using fuzzy logic," Fuzzy Optimization and Decision Making, Springer, vol. 17(4), pages 421-445, December.
    2. Shun-Hung Tsai & Wen-Hui Chen & Ming-Ying Hsiao, 2012. "State-feedback stabilisation for fuzzy bilinear uncertain system with disturbance via fuzzy control approach," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(8), pages 1386-1395.
    3. Liu He & Yuanguo Zhu & Yajing Gu, 2023. "Nonparametric estimation for uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 22(4), pages 697-715, December.
    4. Hadi Vatankhah Ghadim & Mehrdad Tarafdar Hagh & Saeid Ghassem Zadeh, 2023. "Fermat-curve based fuzzy inference system for the fuzzy logic controller performance optimization in load frequency control application," Fuzzy Optimization and Decision Making, Springer, vol. 22(4), pages 555-586, December.
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