Sliding Mode Control for Uncertain Time Delay Systems Based on T-S Fuzzy Model

The fuzzy sliding mode control problem is studied for a class of uncertain nonlinear systems with time delay. The Takagi-Sugeno (T-S) fuzzy model is employed to represent the uncertain nonlinear systems with time delay. By using a novel virtual state feedback technique and linear matrix inequalities (LMI), sufficient conditions for design of robust sliding mode plane are given based on the Lyapunov theory. Design of the sliding mode controller based on reaching law concept is developed, which to ensures system trajectories from any initial conditions asymptotically convergent to sliding mode plane. Therefore, the overall asymptotic stability of the fuzzy sliding mode control system is guaranteed. A numerical example with simulation results is given to illustrate the effectiveness of the proposed method