Discrete-time sliding mode control of nonlinear time-delay systems based on T-S fuzzy model

This paper presents the method of discrete-time sliding mode control (DT-SMC) for a class of nonlinear time-delay systems via Takagi-Sugeno (T-S) fuzzy model. First, the discrete-time linear model with uncertainties and tine-varying delay is derived by employing T-S model to represent original system. Then the control problem becomes the robust stabilization controller design for linear uncertain system with interval time-varying delay. By using the linear matrix inequality (LMI) technique, a sufficient condition for the existence of stable sliding surface depending on the lower and upper delay bounds, is established. On basis of this existence condition, the synthesized discrete-time sliding mode controller can guarantee the sliding mode reaching condition of the specified discrete-time sliding surface. Finally, an illustrative example of truck-trailer is presented to show the correctness and effectiveness of the proposed method.