A behavioral approach to control related analysis of discrete linear repetitive processes

Repetitive processes are a distinct class of 2D systems (i.e. information propagation occurs in two independent directions) of both systems theoretic and applications interest. The feature which makes them distinct from other classes of 2D systems is that information propagation in one of the two independent directions only occurs over a finite duration. Discrete linear repetitive processes are a very important sub-class and in this paper we study them in the behavioral setting. In particular, we show that the key systems properties of stability and controllability are naturally characterized in this setting by means of algebraic conditions on the matrices which define the model.