Design of Robust Fuzzy Sliding-Mode Controller for a Class of Uncertain Takagi-Sugeno Nonlinear Systems

This paper presents the fuzzy design of sliding mode control (SMC) for nonlinear systems with uncertainties, which. can be represented by a Takagi-Sugeno (T-S) model. There exist the parameter uncertainties in both state and input matrices, as well as the matched external disturbance. The key feature of this work is the great ability of the controller to deal with systems without assuming that the control matrices of each local T-S model to be same and knowing the priori information of the upper norm-bounds of uncertainties. A sufficient condition for the existence of the desired fuzzy SMC is obtained by solving a set of linear matrix inequalities (LMIs). The reachability of the specified sliding surface is proven. A numerical example is illustrated in order to show the validity of the proposed scheme.