Many industrial processes involve the processing of a single workpiece by successively passing it through a sequence of machines. The most common example is metal rolling where the metal strip of finite length is shaped by passing it through different sets of rolls and the output from one forms the input to the next and so on. In this paper, we develop a new approach to the analysis and overall control of such systems by first modelling them as a linear repetitive process with switched dynamics. The end result is control law design algorithms which can be implemented using LMI based computations.