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Repetitive controllers represent an attractive solution for systems having periodic reference or disturbance signals with high harmonic content. In order to obtain some performance improvements for three-phase plants, as grid-connected converters, complex repetitive controllers were proposed later in literature. In this article, the advantages of complex repetitive control systems over the real ones are analyzed. In addition, sufficient conditions for the input–output stability of complex repetitive control systems and modified complex repetitive control systems are obtained from the small gain theorem. These stability conditions are then used to derive the stability domains for complex repetitive control systems. Further, a relative stability analysis based on the sensitivity function is introduced. An experimental application based on an active power filter is used to exemplify the effectiveness of the proposed stability analysis. [ABSTRACT FROM AUTHOR]