Parametrization of all regularly implementing controllers

In this short paper we deal with problems of controllerparametrization in the context of behavioral systems. Given a fullplant behavior, a subbehavior of the manifest plant behavior iscalled regularly implementable if it can be achieved as thecontrolled behavior resulting from the interconnection of the fullplant behavior with a suitable controller behavior, in such a waythat the number of outputs of the full controlled behavior is equalto the sum of the number of outputs of the full plant and thenumber of outputs of the controller. For the full interconnectioncase, we establish a parametrization of all controllers thatregularly implement a given behavior. This result is used toobtain a parametrization of all stabilizing controllers. For thepartial interconnection case we present a theorem that reduces theparametrization problem to the full interconnect