Discrete-Time Sliding Mode Control of Nonlinear Systems

The control problem of nonlinear discrete-time systems based on the Takagi-Sugeno (T-S) fuzzy model was addressed. A nonlinear system dynamic model is represented by a T-S fuzzy model. The global T-S fuzzy model of nonlinear system was transformed into linear uncertain system model. So the stabilization problem of nonlinear systems becomes the robust stabilization problem of linear uncertain systems. Discrete-time sliding mode control approach was employed to guarantee robust stabilization of linear uncertain systems. The stable sliding surface was designed by using linear matrix inequalities to reduce the influence of mismatched uncertainties. The sufficient condition for the existence of stable sliding surface was derived in terms of LMI. Moreover the design of sliding mode control law was presented also. The system robust stabilization can be guaranteed and the chattering around the sliding surface in sliding mode control was obviously reduced by the proposed design approach. At last, an illustrative example of truck-trailer was presented to show the feasibility and effectiveness of the proposed method.