A stability analysis method for nonlinear systems with fuzzy logic controller

This paper presented a stability analysis method for nonlinear processes with Takagi-Sugeno's (T-S) fuzzy logic controllers (FLC's). The design of FLC is based on heuristic fuzzy rules. The stability analysis of this fuzzy control model is performed using Krasovskii-LaSalle invariant set theorem with quadratic Lyapunov candidate function. This paper proves that if the Lyapunov function is negative semi-definite in the active region of each fuzzy rule then, the overall system is asymptotic stable in the sense of Lyapunov (ISL). The stability theorem presents in this paper assures sufficient conditions for the stability of the nonlinear system with FLC. The end of the paper contains an illustrative example that describes an application of the method of the stability analysis.