Piecewise-reaching-law based discrete variable structure repetitive control

This paper presents a piecewise-reaching variable structure repetitive control method for uncertain discrete-time linear system. As for the reaching law approach, one needs to modify the original reaching law, as the resultant error dynamics depend on the system uncertainties, By embedding the performance measure of uncertainty rejection into the reaching law to form the ideal switching dynamics, the design of repetitive control can eliminate the periodic disturbances effectively. The control performance will mainly depend on the non-periodic uncertainties. In order to establish stability and convergence of the closed-loop system, the monotone convergence layer, absolute convergence layer and quasi-sliding mode are discussed, and the detailed derivations are given. Numerical simulations are presented to verify the effectiveness of the proposed repetitive control scheme.