Dynamic stabilization of regular linear systems

We consider a general class of infinite-dimensional linear systems, called regular linear systems, for which convenient representations are known to exist both in time and in frequency domain. For this class of systems, we investigate the concepts of stabilizability and detectability, in particular, their invariance under feedback and their relationship to exponential stability. We introduce two concepts of dynamic stabilization, the first formulated as usual, with the plant and the controller connected in feedback, and the second with two feedback loops. Even for finite-dimensional systems, the second concept, stabilization with an internal loop in the controller, is more general. We argue that the more general concept is the natural one, and we derive sufficient conditions under which an observer-based stabilizing controller with an internal loop can be constructed.