Feedback stabilization: the algebraic view

Abstract Based on an abstract algebraic setting we provide an elementary derivation of the Youla-Kucera parametrization of stabilizing controllers and also an alternative, coordinate free, approach of the problem. For this latter case, in contrast to the Youla-Kucera approach, the parameter set is not universal but its elements can be generated by a universal algorithm. We also emphasise the natural continuity property of this parametrization compared to the Youla-Kucera case. Extending the framework to the LFT loops we show by using elementary tools that every controller which stabilizes the interior loop of the generalized plant also stabilizes the LFT loop.