Optimal Guaranteed Cost Control for a Class of Uncertain Fuzzy Systems via Piecewise Quadratic Lyapunov Function Approach

This paper deals with the guaranteed cost control of a class of Takagi-Sugeno (T-S) fuzzy systems with norm-bounded parametric uncertainties via the piecewise quadratic Lyapunov function (PQLF). A linear quadratic cost function is considered as a performance index of closed-loop fuzzy systems. Then, based on the PQLF approach, a robust optimal guaranteed cost control law for stabilization of closed-loop fuzzy systems is derived in the form of linear matrix inequality (LMI). A piecewise parallel distributed compensation (PDC) scheme, which contains the structural information of the rule base as the PQLF is introduced. It is shown that the controller designed by the PQLF approach is robust against norm-bounded parametric uncertainties and has better performance than those of the common quadratic Lyapunov function (CQLF) approach. A numerical example illustrates the efficiency of the PQLF approach and the PDC stabilization method.