An Improved Fuzzy Controller Design via Higher Order Derivatives of Lyapunov Function for Takagi-Sugeno Fuzzy System

This paper is on the issues of designing fuzzy controllers for Takagi-Sugeno fuzzy systems. Many works on the stability and stabilization problems on Takagi-Sugeno fuzzy systems have been done. In the literature, stabilization conditions for Takagi-Sugeno fuzzy system have been improved and their feasibility range has been extended. However, there remains room for reducing the conservativeness for such stabilization conditions. In this paper, we propose a new fuzzy controller design via higher order derivatives of a Lyapunov function with an integral of the membership functions, which drastically reduces the existing conservative stabilization conditions. Finally, a comparison with previous studies is presented to demonstrate the effectiveness of our proposed control method.