On H∞ optimal repetitive controllers

In this paper we consider a two degree of freedom repetitive controller design for a SISO finite dimensional plant. We pose an H^∞ optimal control problem, which we then convert to a two block problem involving a MIMO plant with a scalar time delay, by constraining the solution to have a certain “standard” repetitive structure. We solve a generalization of this two block infinite dimensional MIMO H^∞ optimal control problem by an extension/modification of results for similar SISO systems. The resulting two degree of freedom H^∞ optimal repetitive controller leads to a more general repetitive control structure