Parametrization of All Regularly Implementing Controllers

In this short 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 number of outputs of the full controlled behavior is equal to the sum of the number of outputs of the full plant and the number of outputs of the controller. For the full interconnection case, we establish a parametrization of all controllers that regularly implement a given behavior. This result is used to obtain a parametrization of all stabilizing controllers. For the partial interconnection case we present a theorem that reduces the parametrization problem to the full interconnection case. Copyright c ©2005 IFAC.