State Feedback Fuzzy SMC of Continuous-Time Nonlinear Systems

This chapter studies the state feedback fuzzy SMC problem of continuous-time nonlinear 1-D systems with exogenous disturbances and mismatched parameter uncertainties through T-S fuzzy affine models. In view of the local models sharing one common control input matrix or not, two state feedback SMC design methods are proposed. Firstly, the stability analysis of the sliding motion will be analyzed based on a CQLF and PQLFs , respectively, and the sliding surface gain can be calculated efficiently by solving a set of linear matrix inequalities (LMIs). Then two sliding mode controllers will be designed to ensure that the sliding surface can be reached in finite time. Note that the dynamic SMC method can also handle the mismatched external disturbance. Finally, simulation studies are given to verify the effectiveness of the proposed methods.