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Global non-quadratic D-stabilization of Takagi–Sugeno systems with piecewise continuous membership functions

Author

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  • Cherifi, Abdelmadjid
  • Guelton, Kevin
  • Arcese, Laurent
  • Leite, Valter J.S.

Abstract

This paper deals with the non-quadratic stabilization of Takagi–Sugeno (T-S) models with D-stability constraints. Based on a recently proposed Non-Quadratic Lyapunov Function (NQLF), which involves the mean values of the membership functions (MFs) over a given time interval, three theorems are proposed for the design of non-Parallel Distributed Compensation (non-PDC) controllers satisfying closed-loop D-stability specifications. Despite previous non-quadratic approaches and thanks to the nature of the considered NQLF, it is highlighted that the proposed LMI-based procedures not only apply for the global non-quadratic D-stabilization of T-S models, but also for a larger class of T-S models with piecewise membership functions (i.e. a class of switching nonlinear systems), since no requirement is needed regarding to the bounds of the MFs derivatives. The effectiveness of the proposed LMI-based conditions and their relative degrees of conservatism, compared with previous quadratic D-stabilization results, are illustrated through an academic example involving piecewise membership functions.

Suggested Citation

  • Cherifi, Abdelmadjid & Guelton, Kevin & Arcese, Laurent & Leite, Valter J.S., 2019. "Global non-quadratic D-stabilization of Takagi–Sugeno systems with piecewise continuous membership functions," Applied Mathematics and Computation, Elsevier, vol. 351(C), pages 23-36.
    • Handle: RePEc:eee:apmaco:v:351:y:2019:i:c:p:23-36
    DOI: 10.1016/j.amc.2019.01.031
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