Interconnection and Decomposition Problems with Multidimensional Behaviors

In the behavioral approach, the notion of interconnection is the basis of control. In this setting, feedback interconnection of systems is based on the still more fundamental concept of regular interconnection, which has been introduced by J.C. Willems. This paper deals with multidimensional systems, in particular systems described by linear, constant coefficient partial differential equations. The following problem is addressed: given a plant, under what conditions does there exist a controller such that their interconnection is regular, and has finite codimension with respect to a certain desired system. If it exists, provide a constructive solution to the problem. The second part of this paper treats the related problem of decomposition of systems. First, we study the problem of decomposing the system into its controllable part and an autonomous subsystem, and finally we study decompositions of the controllable part.