This paper presents linear quadratic (LQ) repetitive control (RC) methods for processes represented by a conventional FIR model and a circulant FIR model. The latter, which represents a FIR system under the assumption of a cyclic steady state, is named as such as its input-output map is represented by a circulant matrix. Using the complete frequency resolving property of a circulant matrix, a special tuning method for the LQ weights is proposed. Performance of the proposed method is investigated through numerical examples. (C) 2008 Elsevier Ltd. All rights reserved.