More Relaxed Stability Conditions for Fuzzy TS Control Systems by Optimal Determination of Membership Function Information

Abstract

In this paper, a systematic and optimal approach is presented for more relaxed stability analysis conditions and controller design for Takagi-Sugeno systems. The approach is based on the idea of non-quadratic Lyapunov function. The non-quadratic Lyapunov function is a fuzzy blending of multiple quadratic Lyapunov function. The weak point of non-quadratic Lyapunov function is that the upper bounds of time derivative of membership functions is considered known or selected by trial and error. In this paper, the upper bounds are determined based on the concept of decay rate and control input constraint. In contrast to the existing work based on non-quadratic Lyapunov function, the proposed method leads to more relaxed stability analysis conditions and wider stability region by optimal calculation of the upper bounds of the time derivative of membership functions. The proposed approach provides a stable closed loop control system with faster response and less control effort along with wider stability region in terms of system parameters variations. Several numeric examples and comparisons illustrate the effectiveness and superiority of the proposed method.