Membership-Functions-Derivative-Dependent Stability Criteria for Delayed Takagi–Sugeno Fuzzy Systems

The stability of delayed Takagi–Sugeno fuzzy systems is addressed under membership functions related to time or the system states. In the case where membership functions are correlated with time, improvements are made to existing stability criteria, specifically those reliant solely on the upper bounds of the membership functions' derivative. After constructing the fuzzy Lyapunov–Krasovskii functional, common integral terms are given to compensate for fuzzy integral terms, and free-weighting matrices are incorporated. Consequently, concerned with the unique trait of membership functions, the membership-functions-derivative-dependent stability criteria are derived. These criteria consider both precise upper and lower bounds of the membership functions' derivative, resulting in less conservatism compared with the previous criteria that only contained upper bounds. Moreover, by fully incorporating fuzzy information in the derivatives of fuzzy integral terms, a local stability criterion with reduced conservatism is obtained under membership functions associated with the system states. Ultimately, the efficacy and merits of the presented approach are substantiated through numerical examples.