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Most current repetitive controllers apply the internal model principle by embedding a one-period delay into the control scheme. While being simple and often effective, this structure involves a number of disadvantages: (i) in many applications, large memory buffers are needed; (ii) information about the spectrum of the periodic input cannot be included and (iii) accounting for period-time uncertainty results in controllers that are overly robust for lower harmonic frequencies. In order to overcome these disadvantages, the present paper proposes a novel repetitive controller structure that sacrifices the simplicity of the one-period delay structure for the benefit of more design freedom. The resulting generalized repetitive controller encompasses the one-period delay structure as a special case and is designed based on semidefinite programming. Numerical results reveal that a generalized repetitive controller yields significantly better performance with the same amount of memory or, conversely, requires substantially less memory to achieve equivalent performance.