On a generalization of the Youla-Kučera parametrization. Part I: the fractional ideal approach to SISO systems

In this paper, we show how to use the theory of fractional ideals in order to study the fractional representation approach to analysis and synthesis problems for SISO systems. Within this mathematical framework, we give necessary and su8cient conditions so that a plant is internally/strongly/bistably stabilizable or admits a (weak) coprime factorization. Moreover, we show how to generalize the Youla–Ku' cera parametrization of the stabilizing controllers to any stabilizable plant which does not necessarily admit a coprime factorization. This parametrization is generally a8ne in two free parameters. c © 2003 Elsevier B.V. All rights reserved.