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.