A Sequence of Finite-Dimensional Controllers for Repetitive Control of Positive Real Systems

In this paper, we analyze the performance of positive real plants coupled with a progressively increasing number of harmonic oscillators. We prove that, as the number of oscillators tends to infinity thus covering the all frequency range, the steady-state output weakly converges to the periodic signal to be tracked. On the basis of this result, we next show that, under a suitable constraint on the signal to be tracked, strong convergence is actually achieved.