Abstract Iterative learning control has been developed for systems that repeat the same task over a finite duration with resetting to the starting location once each repetition, or trial, is complete. The novel feature is the use of information generated on the previous trial to compute the control input for the next one and the basic problem is to force the sequence of trial outputs to track a given reference signal. In many cases, it is also necessary to regulate the dynamics produced along the trials, for which this paper gives new results using the theory of linear repetitive processes and the generalized form of the Kalman-Yakubovich-Popov lemma.