A larger family of nonlinear systems for the repetitive learning control

A generalization of the PIDρ−1ρ−1 control has been recently presented in Marino et al. (2012), which guarantees the output tracking of smooth periodic reference signals (with known period) for uncertain minimum phase nonlinear systems in output feedback form with any relative degree ρ≥1ρ≥1. In this note, we show that the repetitive learning control proposed in Marino et al. (2012) also solves the same output tracking problem for a larger class of uncertain nonlinear systems in normal form, provided that the inverse system dynamics satisfy the Demidovich condition on suitable compact sets.