Author\´s reply [to comments on "Nonlinear repetitive control"]

Our paper (Ghosh and Paden, "Nonlinear repetitive control", IEEE Trans. Automat. Contr., vol. 45, p. 949-54, 2000) proves Theorem 1, which establishes conditions for the stability of the nonlinear repetitive control system, and Proposition 2, which goes on to establish bounds on the steady-state error signals. These are correct as stated as they apply to repetitive controllers with a finite number of oscillators in their internal model. An issue correctly raised in the commentary (Lucibello, "Comments on \´Nonlinear repetitive control\´", IEEE Trans. Automat. Contr., vol. 48, p. 1470-1, 2003) is that the conditions of Proposition 2 might be difficult to meet when the number of oscillators is large. This observation does not challenge the veracity of the proposition, but is certainly insightful. In our introductory comments of Section 11, we attempt, and fail, to make a qualitative connection to the pure time delay type repetitive control. The following statement is incorrect and should be deleted from our paper: "This justifies the fact that in the limit N → ∞, the above model of the repetitive controller, works as well as the ideal model in achieving perfect tracking for typical reference signals".