Abstract
In this paper, we discuss convergence of iterative learning control based on the gradient method for linear discrete-time systems. First, it is shown that residuals generated by the algorithm converge exponentially and therefore, observation errors or disturbance does not cause divergence. Second, the convergence conditions are expressed as strictly positive realness of the ratio of transfer functions. Conditions for the strictly positive realness is presented when there exists uncertainty of parameters in the transfer function and it is known that they are in given intervals. We also propose a simple sufficient condition for the strictly positive realness, which is based on a special structure of the problem. Finally, we illustrate design procedure based on the results given in this paper. Applications of the results to sampled-data systems are also discussed.
