A new fuzzy Lyapunov function approach for a Takagi–Sugeno fuzzy control system design

In this paper, a new fuzzy Lyapunov function approach is presented for a class of continuous-time Takagi–Sugeno fuzzy control system. The proposed fuzzy Lyapunov function is formulated as a line-integral of a fuzzy vector which is a function of the state, and it can be regarded as the work done from the origin to the current state in the fuzzy vector field. Unlike the approaches using a fuzzy blending of multiple quadratic Lyapunov functions, the time-derivatives of membership functions do not appear in the proposed approach. The effectiveness of the proposed approach is shown through numerical examples.