Design of sliding mode controller for MIMO system

Based on the Lyapunov stability theorem, a design methodology of the sliding mode control for a class of MIMO systems with mismatched perturbations as well as input uncertainty are proposed to solve regulation problems. When the dynamics of the controlled system enter the sliding surface, the state trajectories of the system can achieve asymptotical stability even if the mismatched perturbations exist. The proposed controller is designed under the requirement that the designers need some knowledge of the upper bounds of perturbations, and it has the ability to drive the state´s trajectory into the designated sliding surface in a finite time.