Discrete time sliding mode control with minimal quasi sliding mode band

A new approach is presented to analyze sliding mode control in discrete-time systems using an established reaching law, whereby the ultimate band is obtained to be lesser than any previous analysis done with the same reaching law. Also, the controller parameters are evaluated according to the ultimate band that is desired. The approach begins with defining several bands in the space of the surface variable, which are key to understanding the dynamics of it. Conditions on these band values are key to assigning appropriate values to the controller parameters. The switching gain obtained in this way comes out to be negative contradicting popular notion of non-negative switching gains used in sliding mode control. A case is also studied where the states measured contribute a quantization error in the system dynamics. The idea developed in analyzing the case without quantization is used while dealing with it.