An Algorithm for Stability of Takagi–Sugeno Fuzzy Logic Controller

This paper presents the design of fuzzy logic controllers (FLC’s) for nonlinear systems. Fuzzy logic control systems consist of a plant and a fuzzy logic controller. The output of the FLC is made by 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 become highly non-linear and the analysis of system stability for this system are 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 stable in the sense of Lyapunov under common Lyapunov function, the overall system is also stable in the sense of Lyapunov.