Robust H∞-sliding mode control for a class of nonlinear systems with mismatched uncertainties

In this paper a robust H
_∞
-sliding mode control is proposed for controlling a class of nonlinear systems with mismatched parametric uncertainty and external disturbance. Based on Lyapunov stability theorem, the proposed control scheme can achieve both asymptotic stability and H
_∞
performance in the sliding mode by giving new existence condition of switching surface in terms of LMIs. Then, a robust controller that assures the occurrence of the sliding mode in finite time is developed. Finally, a numerical example is given to demonstrate the effectiveness of results.