Sliding mode control for mismatched discrete singular systems with dynamic disturbance compensator

Synthesis problem of sliding mode control (SMC) for mismatched discrete singular systems (DSS) with internal parameter perturbation and external disturbance is considered. Dynamic switching function with last step state vector is given to guarantee the stability of the control system in the switching band. Discrete singular reaching law with dynamic disturbance compensator is designed to eliminate the restriction of the system uncertainties is bounded and the satisfaction of matching conditions compared with conventional SMC and provides essential condition of quasi-sliding mode which can cross the switching plane step by step. Discrete singular sliding mode controller is designed by applying the reaching law, which can guarantee the system to reach the switching plane in finite time, decrease the system chattering effectively and enhance the dynamic quality of the system. A numerical example illustrates the feasibility and validity of the proposed approach.