Open Journal of Applied Sciences

Volume 12, Issue 11 (November 2022)

ISSN Print: 2165-3917   ISSN Online: 2165-3925

Google-based Impact Factor: 1  Citations  

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

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DOI: 10.4236/ojapps.2022.1211126    151 Downloads   547 Views  Citations

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.

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Zeng, J. and Bao, L. (2022) Asymptotically Necessary and Sufficient Quadratic Stability Conditions of T-S Fuzzy Systems Using Staircase Membership Function and Basic Inequality. Open Journal of Applied Sciences, 12, 1824-1836. doi: 10.4236/ojapps.2022.1211126.

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