Strongly autonomous interconnections and stabilization of 2D behaviors

In this paper we study linear discrete two-dimensional systems in the behavioral context where control is viewed as interconnection. Within this framework the natural concept of regular interconnection has been introduced by J.C.Willems. Here we investigate regular interconnections that yield finite dimensional behaviors using tools previously developed to analyze almost implementation problems. We prove that when a finite dimensional (sub-) behavior can be achieved from a given behavior by regular interconnection then the controllable part of the original behavior is rectifiable, moreover, in this case all the other sub-behaviors are almost regularly implementable. We apply these results to characterize all stabilizable behaviors.

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