Stability of equivalent control based discrete sliding mode controller

In this paper, the stability condition of a discretized sliding mode control system is studied. For the conventional system, the stability of the closed-loop system is dependent on the sampling time, i.e., it turns to be unstable over a sampling period, and is stable under the sampling period. For the given system, however, it is shown that the interval of stable and unstable sampling periods appears alternately. It is also shown that the stability of the overall system can be predicted by checking up the magnitude of one parameter of the discretized system.