The canonical controllers and regular interconnection

We study the control problem from the point of view of the behavioral systems theory. Two controller constructions, called canonical controllers, are introduced. We prove that for linear time-invariant behaviors, the canonical controllers implement the desired behavior if and only if there exists a controller that implements it. We also investigate the regularity of the canonical controllers, and establish the fact that they are maximally irregular. This means a canonical controller is regular if and only if every other controller that implements the desired behavior is regular.