Switching-function dynamics based design of sliding mode repetitive controllers

This paper addresses the problem of repetitive control for systems in which the reference input is a periodic signal, with known a period. The sliding mode repetitive controller based on switching-function dynamics is designed to eliminate the disturbances with the same period. In exponential reaching law, the sign function is replaced with power item to decrease chattering and a measure of disturbance-rejection is embedded in so as to solve the system uncertainties. In order to characterize the performance of closed system, monotone decreasing area boundary and absolute convergence layer boundary of switching-variate are defined and the bounds are derived in details.