Harnessing membership function dynamics for stability analysis of T-S fuzzy systems

The main goal of this paper is to develop a new less conservative linear matrix inequality (LMI) condition for the asymptotic stability of continuous-time Takagi-Sugeno fuzzy systems. A key advantage of this new condition is its independence from the bounds on the time-derivatives of the membership functions (MFs), a requirement that presents in the existing approaches. This is achieved by introducing a novel fuzzy Lyapunov function that incorporates an augmented state vector. Notably, this augmented state vector includes MFs and allows their dynamics to be integrated into the proposed LMI condition. This inclusion of additional information about MFs reduces the conservativeness of the suggested stability condition. Finally, examples are given to demonstrate the effectiveness of the proposed method.