z-Transform and Volterra Operator Based Approaches to Controllability and Observability Analysis for Discrete Linear Repetitive Processes

Linear repetitive processes are a distinct class of 2D systems of both systems theoretic and applications interest. They are distinct from other classes of such systems by the fact that information propagation in one of the two separate directions only occurs over a finite duration. This, in turn, means that existing 2D systems theory either cannot be applied at all or only in substantially modified form. Hence a distinct systems theory must be developed for them with onward translation (where appropriate) into reliable routinely applicable analysis and design tools. This paper contributes substantial news results to this general task in the areas of controllability and observability for the sub-class of so-called discrete linear repetitive processes which arise in key applications areas and, in particular, iterative learning control