Finite dimensional interconnections and stabilization of 2D behaviors

This paper deals with discrete two-dimensional behaviors which are described by linear systems of partial difference equations with constant coefficients. Within the behavioral framework a natural concept of interconnection has been introduced by J.C.Willems, called regular interconnection. We investigate regular interconnections that yield finite dimensional behaviors, and prove that when a finite dimensional behavior can be achieved from a given behavior ℬ by regular interconnection then the controllable part of ℬ is rectifiable. We apply this result to characterize all stabilizable behaviors.