On the existence of stabilizing compensation

Of fundamental importance in the theory of linear invariant systems are the conditions under which one can find a feedback controller which will result in a stable closed-loop system, whether the plant is stable or not. This correspondence proves the intuitively reasonable proposition that observability of the unstable modes of the plant by the available measurements, and controllability of these unstable modes by the control constitute necessary and sufficient conditions for the existence of a compensator which stabilizes the closed-loop system.