A fractional ideal approach to stabilization problems

The purpose of this paper is to show how the theory of fractional ideals is a powerful mathematical framework for the study of stabilization problems of linear SISO systems. In particular, in terms of fractional ideals, we give necessary and sufficient conditions for a plant to be internally/strongly/bistably stabilizable or to admit a (weakly) coprime factorization. Finally, we show how to extend the Youla-Kučera parametrization of all stabilizing controllers to every stabilizable plant which does not (necessarily) admit coprime factorizations.