The synthesis problem of designing sliding mode variable structure control(VSC) is considered for Delta operator
systems. First of all, a sufficient condition for the existence of linear sliding surface in terms of linear matrix inequality(LMI)
approach is given, and the proposed approach brings previous related conclusions of continuous systems and discrete-time
systems into unified Delta operator systems. Sliding mode VSC strategy for Delta operator systems is obtained by employing
exponential reaching law. Then, variable structure controller for a class of uncertain Delta operator systems with internal
parameter perturbation and external disturbance is designed, and the asymptotic stability of quasi-sliding mode is proved.
Good dynamic properties can be obtained at the same time. Finally, under the premise of the very small sampling period, the
simulation result shows the feasibility and effectiveness of the proposed approach.