A new repetitive control scheme is proposed for tracking control of systems with reference signals which are not necessarily time periodic functions. The L-2-stability of the closed-loop system is rigorously proved by using operator theory in functional analysis and moreover it is shown that under certain conditions, the tracking error converges to zero asymptotically. The proposed control scheme is applied to the tracking control of an AC motor, and simulation and experimental results are presented to show the effectiveness of the new repetitive control scheme.