Robust sliding mode-H∞ control for a class of unmatched systems

In this paper, a robust sliding mode-H
_∞
control design method for a class of nonlinear systems with unmatched external disturbance is proposed. The design procedure combines the high robustness of the sliding mode control (SMC) with the H
_∞
norm performance. First, a novel result for switching surface design is derived in terms of linear matrix inequalities (LMIs). Then, a robust controller that assures the occurrence of the sliding mode in finite time is proposed. Finally, the validity of the design method is proved by simulation results.