Stabilization of a class of fuzzy control systems via piecewise fuzzy Lyapunov function approach

This paper deals with the stability analysis and stabilization of a class of Takagi-Sugeno (T-S) fuzzy systems via piecewise fuzzy Lyapunov function approach. The piecewise fuzzy Lyapunov function is proposed by utilizing the structure information of the rule premise. Based on this function approach, sufficient conditions for stabilization of both open-loop fuzzy systems and closed-loop fuzzy systems are derived in the form of linear matrix inequality (LMI). A piecewise parallel distributed compensation (PDC) scheme which also contains the information of the rule base is introduced. It is shown that the piecewise fuzzy Lyapunov function approach is less conservative than those of the common Lyapunov function and the piecewise Lyapunov function. Some numerical examples illustrate the efficiency of the piecewise fuzzy Lyapunov function approach and the PDC stabilization method.