Optimal sliding mode control for linear discrete singular system

The optimal sliding mode surface and variable structure control (VSC) are proposed for linear discrete singular system. Firstly, the system is decomposed into two low dimensional subsystems by a restricted system equivalent decomposed method. Secondly, the sliding mode controller is designed based on the restricted equivalent subsystems. The quadratic performance index optimal control technique is introduced to design the optimal sliding mode. By applying reaching law approach, the selected control law ensures that the solution trajectories of the system reach the switching surface in finite time and have low chattering in the sliding motion. Finally, a simulation example is given to illustrate the feasibility and validity of the proposed method.