Optimal sliding mode control for a class of uncertain discrete-time systems

This paper proposes a Discrete Optimal Sliding Mode Control (D-OSMC) algorithm for uncertain linear systems. The parameter uncertainties are assumed to be unknown but norm-bounded. Firstly, for the nominal system, an optimal control law is derived to satisfy linear quadratic performance index. To overcome the problem accompanying the choice of the matrix of the matrix of the sliding surface, a novel method based on the resolution of a Sylvester equation is proposed. In order to ensure the robustness of the system during the reaching phase, a novel optimal discrete integral, sliding surface is designed. Simulation results have been presented to confirm the usefulness and the effectiveness of the proposed control strategy.