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Non-fragile guaranteed cost control for Takagi–Sugeno fuzzy hyperbolic systems

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  • Minglai Chen
  • Junmin Li

Abstract

This paper concerns the problems of non-fragile guaranteed cost control (GCC) for nonlinear systems with or without parameter uncertainties. The Takagi–Sugeno (T–S) fuzzy hyperbolic model is employed to represent the nonlinear system. The non-fragile controller is designed by parallel distributed compensation (PDC) method, and some sufficient conditions are formulated via linear matrix inequalities (LMIs) such that the system is asymptotically stable and the cost function satisfies an upper bound in the presence of the additive controller perturbations. The above approach is also extended to the non-fragile GCC of T–S fuzzy hyperbolic system with parameter uncertainties, and the robust non-fragile GCC scheme is obtained. The main advantage of the non-fragile GCC based on the T–S fuzzy hyperbolic model is that it can achieve small control amplitude via ‘soft’ constraint approach. Finally, a numerical example and the Van de Vusse example are given to illustrate the effectiveness and feasibility of the proposed approach.

Suggested Citation

  • Minglai Chen & Junmin Li, 2015. "Non-fragile guaranteed cost control for Takagi–Sugeno fuzzy hyperbolic systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(9), pages 1614-1627, July.
    • Handle: RePEc:taf:tsysxx:v:46:y:2015:i:9:p:1614-1627
    DOI: 10.1080/00207721.2013.827259
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    References listed on IDEAS

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    1. Tsai, Shun-Hung & Li, Tzuu-Hseng S., 2009. "Robust fuzzy control of a class of fuzzy bilinear systems with time-delay," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2028-2040.
    2. Chen, Bing & Liu, Xiaoping & Tong, Shaocheng, 2008. "Robust fuzzy control of nonlinear systems with input delay," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 894-901.
    3. Dedong Yang & Kai-Yuan Cai, 2011. "Finite-time reliable guaranteed cost fuzzy control for discrete-time nonlinear systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(1), pages 121-128.
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