Industrial processes such as long-wall coal cutting and me-tal rolling, together with certain areas of 2D signal andimage processing, exhibit a repetitive, or multipass struc-ture characterized by a series of sweeps of passes through aknown set of dynamics. The output, or pass profile, producedon each pass explicitly contributes to that produced on thetext. This interpass interaction can lead to the growth ofoscillations, and hence a form of instability, in the se-quence of pass profiles which require control strategiesthat explicitly incorporate the essential repetitive struc-ture of the process in their decision making. This monographis unique in developing the new techniques necessary for sy-stematic control systems design in the form of a stabilitytheory and computationally feasible stability tests based onfinite simulations and polynomial analysis. Its developmentrequires a basic knowledge of linear frequency domain andstate-space theory and a knowledge of basic functional ana-lysis would be beneficial. The text is aimed at researchersin the area of control and systems theory and should also beof interest to those working in the related area of signaland image processing.