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Cao, K., Gao, X.Z., Lam, H.K., Vasilakos, A.V. and Pedrycz, W. (2014) A New Relaxed Stability Condition for Takagi-Sugeno Fuzzy Control Systems Using Quadratic Fuzzy Lyapunov Functions and Staircase Membership Functions. International Journal of Fuzzy Systems, 16, 327-337.

has been cited by the following article:

• TITLE: Asymptotically Necessary and Sufficient Quadratic Stability Conditions of T-S Fuzzy Systems Using Staircase Membership Function and Basic Inequality

  AUTHORS: Jianjian Zeng, Lijuan Bao

  KEYWORDS: Takagi-Sugeno Fuzzy System, Quadratic Stability, Fuzzy Controller, Staircase Membership Function

  JOURNAL NAME: Open Journal of Applied Sciences, Vol.12 No.11, November 17, 2022

  ABSTRACT: Asymptotically necessary and sufficient quadratic stability conditions of Takagi-Sugeno (T-S) fuzzy systems are obtained by utilizing staircase membership functions and a basic inequality. The information of the membership functions is incorporated in the stability analysis by approximating the original continuous membership functions with staircase membership functions. The stability of the T-S fuzzy systems was investigated based on a quadratic Lyapunov function. The asymptotically necessary and sufficient stability conditions in terms of linear matrix inequalities were derived using a basic inequality. A fuzzy controller was also designed based on the stability results. The derivation process of the stability results is straightforward and easy to understand. Case studies confirmed the validity of the obtained stability results.