RESOLUTION TOPOLOGY AND INTERNAL STABILIZATION.

Author considers here a standard regulator problem. This problem has been dealt with by many authors in many different frameworks from the pioneering work of D. C. Youla et al. who gave a parametrization of the class of all stabilizing controllers in the classical frequency domain framework, to the ring theoretic framework of C. A. Desoer et al. Author would like to relate to two inherent difficulties in this framework, the first being conceptual the second technical. The Youla approach to stabilization depends on the existence of co-prime factorizations for the plant. While in the classical frequency domain, in the mathematical framework of rational matrix functions, such factorizations are straightforward, in the operator theoretic framework the class of operators for which such factorizations exist is not known. This, of course, is a purely technical problem and just implies that further research in this area is necessary to complete the theory. The conceptual problem arises from the problem of what plants are considered non-stable for stabilization purposes.