On digital implementation of continuous sliding mode control

The paper presents some new results on digital implementation of sliding mode control when designed from a continuous time system. When a continuous sliding mode control is digitally implemented, it cannot bring the sliding variable to the surface in finite time and stay there, but the sliding variable remains within an ultimate band around the surface. Analysis is done which relates such an ultimate band with the continuous controller parameters. If the controller parameters are chosen accordingly, one can be sure that the sliding motion will remain inside the specified ultimate band, and hence stability can be assured for such a digital implementation of the continuous sliding mode control.