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.