Design & analysis of fuzzy logic controller using Lyapunov function for a non-linear system

In this paper a T-S Fuzzy model (which originates from Takagi and Sugeno) is used to design a fuzzy logic controller (FLC) for non-linear systems. Fuzzy logic control systems consist of a plant and a fuzzy logic controller. The output of the FLC is made by weighted average defuzzification method So, the output of the FLC is a function of the degrees of membership of the fuzzy rules, and these degrees of membership are function of input variables that are the system states. Therefore, the control system becomes highly non-linear and the analysis of system stability for this system is very difficult In this paper, it is proved that if each fuzzy logic control systems consist of a plant and each fuzzy logic rule is asymptotically stable in the sense of Lyapunov under common Lyapunov function, then the overall system is locally stable in the sense of Lyapunov. To show the effectiveness of the proposed technique we have used inverted pendulum, a well known non-linear system.