An alternative notion of a stabilizing controller is presented. Being defined in terms of the trajectories of plant and controller, it is well suited for situations in which the controller’s action is an interconnecting one. In the second part of the paper, a parametrization is given of the kernel representations of all controllers that give rise to an a priori specified closed-loop behavior. As a special case, the parametrization yields all stabilizing controllers. Unlike the Youla parametrization, it also includes the so-called singular stabilizing controllers.