Computer-controlled continuous-time variable structure systems with sliding modes

The implementation problems by a digital computer for a well-designed linear continuous-time variable structure control system are considered. By using the zero-order-hold of the designed continuous-time VSS controller, a corresponding discrete-time controlled system is obtained. For the discrete-time system a new definition, the discrete-time weak-pseudo-sliding mode, is given to describing the zigzag behaviour corresponding to the continuous-time VSS sliding mode. An upper bound of the sampling period is given to guarantee the existence of the weak-pseudo-sliding mode along the prescribed hyperplane for the discrete-time system. If the chosen sampling period is not greater than this upper bound, the zero-order-hold of the continuous-time VSS controller can still stabilize sampled data system without any modification. Finally, simulation results are presented to show the effectiveness of the decision of the upper bound.