This paper introduces a new method for synthesizing multiple-period repetitive controllers. The main innovations in the synthesis procedure presented in this article are two. The first one is that this technique yields a solution compatible with the integration of the computed multiple-period repetitive controller into a minimum-variance adaptive control scheme. The second innovation is that the solution is period-recursive, reducing the complexity of controller synthesis considerably when compared with other methods available in the literature. To exemplify the synthesis procedure, a multiple-period repetitive controller is designed and integrated into an adaptive-repetitive control scheme used in the track-following control of a commercial hard disk drive. Experimental results show the effectiveness of the presented approach. (C) 2010 Elsevier Ltd. All rights reserved.