Industrial processes such as long-wall coal cutting and metal rolling, together with certain areas of 2D signal and image processing, exhibit a repetitive, or multipass structure characterized by a series of sweeps of passes through a known set of dynamics. The output, or pass profile, produced on each pass explicitly contributes to that produced on the next. This interpass interaction can lead to the growth of oscillations, and hence a form of instability, in the sequence of pass profiles, which require control strategies incorporating the essential repetitive structure of the process in their decision-making. This monograph describes new techniques necessary for systematic control of systems design in the form of a stability theory and computationally feasible stability tests based on finite simulations and polynomial analysis. Its development requires of the reader/user a basic knowledge of linear frequency domain and state-space theory and a knowledge of basic functional analysis would be beneficial. This text is intended for the use of researchers in the area of control and systems theory and should also be of interest to those working in the related area of signal and image processing.