Discrete-Time Fuzzy Sliding Mode Control of Nonlinear Systems

This paper addresses the control problem of nonlinear systems based on the Takagi-Sugeno (T-S) fuzzy model. T-S model was adopted for fuzzy modeling of the nonlinear system. The global T-S fuzzy model of nonlinear systems was transformed into linear uncertain system model. So the stability problem of nonlinear systems becomes the robust stabilization problem of linear uncertain systems. Discrete-time sliding mode control approach was employed to guarantee robust stability 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 in terms of LMI was derived and the sliding mode control law was presented also, which guaranteed the global stability of the systems