New 2D models and a transition matrix far discrete linear repetitive processes

This paper reports further results on the development of a control systems theory for discrete linear repetitive processes. In particular, Roesser and Fornasini-Marchesini state space model equivalent descriptions for the dyn amics of these processes are constructed and then used to develop new stabi lity tests which involve only computations on matrices with constant entrie s. Also, they are used to develop a transition matrix, or fundamental matri x sequence, for these processes which is then used to define and characteri se so-called local reachability and controllability properties in the form of matrix rank-based tests.