Algorithms for interconnection and decomposition problems with multidimensional systems

The notion of interconnection is the basis of control in the behavioral approach. 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. In this paper, 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 so, provide a constructive solution to the problem. The second part of the paper treats the related problem of decomposition of systems. First, the autonomous/controllable decomposition is studied, and finally we look at the decomposition of the controllable part.