This paper introduces a new method for synthesizing multiple-period repetitive controllers, which are suitable for integration into a combined adaptive-repetitive control scheme. The proposed synthesis method can be implemented recursively reducing the complexity of controller design considerably when compared with other methods available in the literature. In order to exemplify the synthesis procedure, a multiple-period adaptive-repetitive controller is designed for track-following control of a commercial hard disk drive and implemented in real-time using a digital signal processor. Experimental results show the effectiveness of the approach introduced in this work.