This paper develops significant new results on the design of Iterative Learning Control (ILC) schemes based on treating the problem within the framework of the stability/ control theory for linear repetitive processes. These processes propagate in two independent directions and arise in the modeling of a number of physical processes. The duration of information propagation in one of these two directions is finite, and this is a key link to ILC which has been developed as a technique for controlling systems which are required to repeat the same operation over a finite duration known as the trial length. Each execution of the operation is known as a trial and when it finishes the process resets and the next trial begins. The novel idea in ILC is to use information from previous trials to compute the input to the current one and thereby sequentially improve performance. Previous work has shown that linear model ILC can be described by certain repetitive process models and in this paper the starting point is so-called strong practical stability for these processes. In particular, it is shown how this stability property can be used to design ILC laws in the case when there are performance specifications that require control of the transient dynamics produced along the trials, in addition to trial-to-trial error convergence.