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On the Parametrization of All Regularly Implementing and Stabilizing Controllers

In this paper we deal with problems of controller parametrization in the context of behavioral systems. Given a full plant behavior, a subbehavior of the manifest plant behavior is called regularly implementable if it can be achieved as the controlled behavior resulting from the interconnection of the full plant behavior with a suitable controller behavior, in such a way that the controller does not impose restrictions that are already present in the plant. We establish a parametrization of all controllers that regularly implement a given behavior. We also obtain a parametrization of all stabilizing controllers.