Parameterization of all controllers that stabilize a given plant

A simple and insightful method to teach the Youla-Kučera parameterization of all controllers that stabilize a given plant is presented. The text is intended for first-year graduate students in engineering. The result is derived first using transfer functions. A state-space representation of all stabilizing controllers then naturally evolves from the transfer function result. Thus, the transfer functions and the state-space techniques are presented as connected approaches rather than isolated alternatives.