Abstract
An iterative learning control (ILC) is considered for a linear time-invariant plant. Its discretized system with a sampling period is introduced via delta operator. For this discrete-time plant, a necessary and sufficient condition is given under which its tracking error converges to zero as the number of iterations goes to infinity. Then, a sufficient condition of convergence of ILC for the original continuous-time plant is derived by considering the case that the sampling period tends to zero. The condition is that the spectral radius of a matrix is less than one, while the existing condition is that an induced norm of the matrix is less than one. Since the spectral radius of a matrix is always less than or equal to any induced norm of the matrix, the convergence condition of this paper is better than any other condition based on induced norm.
