In many engineering problems, periodic signals which should be either tracked (reference signals) or rejected (disturbances) occur. A successful way of solving such problems is repetitive control, a well-known technique based on the internal model principle. Here, we extend repetitive control theory to plants with several outputs, of which only some have to track reference signals. The other outputs are used to supply additional information to the controller. We analyze stability, robustness and give estimates of the size of the error in such a feedback system. Our approach to this analysis is new, based on the recent theory of regular linear systems. We introduce a correction to the amount of delay used in the internal model and this leads to a significant improvement in performance (i.e., to a smaller error).