Stability analysis for multi-periodic repetitive control systems

The paper considers the problem of rejection of a general multi-periodic disturbance. The general multi-periodic disturbance is a superposition of multiple general periodic disturbances. Assume that the periods of the periodic disturbances are known. Under the condition that the unperturbed system is positive real, we present a new method for rejection of a multi-periodic general disturbance, which is based on the estimation of the disturbance. It is showed that the state variables in the closed loop system converge to zero. Finally, an example is presented to show the utility of the method.