Regular feedback implementability of behaviors

In this paper we address the problem of impulses that might occur when a to-be-controlled plant is connected to a suitable controller. In the behavioral literature, this problem is known to be closely related to so-called the ´regular feedback interconnection´ (RFI) of the plant behavior and the controller behavior. This paper contains some results about inadmissibility of some initial conditions and its relation to RFI. We also address the question of when a given controlled behavior can be obtained by RFI of the given plant and some suitable controller. The paper contains a necessary condition for the existence of a controller that achieves the given controlled behavior by RFI. This necessary condition is utilized in an algorithm that terminates into one of two cases: either a specific controller that achieves the controlled behavior by RFI or the conclusion that such a controller does not exist, thus resulting in a necessary and sufficient condition to check regular feedback implementability. Finally, we find all the controllers that achieve the controlled behavior by RFI with respect to the plant behavior.