Research for Discrete Variable Structure Control Systems

A combined control scheme is proposed in this paper for linear discrete-time systems. It takes account of not only dynamic performance on the sliding mode but also the dynamic performance in the reaching phase. The whole phase is divided into two big regions: the reaching region and a small selected boundary layer related with original sampling interval. In the reaching region, the optimal control of linear quadratic form is applied; inside the boundary layer, the sampling interval is changed and a combined reaching law of sliding mode control is used, thus the discretization chattering is eliminated more or less. Then the final quasi-sliding mode is proved to be asymptotically stable by Lyapunov methods. An example establishes the effectiveness of this combined controller.