Stability Analysis Method for Fuzzy Control Systems Dedicated Controlling Nonlinear Processes

This paper presents a new stability analysis method for nonlinear processes withTakagi-Sugeno (T-S) fuzzy logic controllers (FLCs). The design of the FLCs is based onheuristic fuzzy rules. The stability analysis of these fuzzy control systems is performed usingLaSalle’s invariant set principle with non-quadratic Lyapunov candidate function. Thispaper proves that if the derivative of Lyapunov function is negative semi-definite in theactive region of each fuzzy rule, then the overall system will be asymptotically stable in thesense of Lyapunov (ISL). The stability theorem suggested in the paper ensures sufficientstability conditions for fuzzy control systems controlling a class of nonlinear processes. Theend of the paper contains an illustrative example that describes an application of thestability analysis method.