Convergence conditions of iterative learning control revisited: A unified viewpoint to continuous-time and discrete-time cases

This paper deals with convergence conditions of iterative learning control (ILC) for linear time-varying plants from a unified viewpoint to continuous-time and discrete-time cases. For a continuous-time plant, the corresponding discrete-time plant with a sampling period is obtained via delta operator. Then, a necessary and sufficient condition is given under which the tracking error of the discrete-time ILC converges to zero as the number of iterations tends to infinity. A candidate of ILC convergence condition for the original continuous-time plant is readily obtained by considering the case that the sampling period tends to zero. It is in fact a sufficient condition of convergence, which is shown with a rigorous proof. The condition is based on the supremum of the set of the spectral radius of a time-varying matrix related to the feedthrough term of the plant to its differential output. It is better than any other existing conditions based on induced norm.