A new parameterization of all stabilizing controllers in a SISO setup

Youla-Parameterization has been widely utilized in control system analysis and control system design. In this approach, all stabilizing controllers are parameterized by a stable transfer function. However, there also exists a different parameterization approach and when applied to scalar feedback active control systems, it possesses remarkable properties: it not only parameterizes all stabilizing controllers, but also parameterizes performance variables that allow a geometric interpretation. This note aims to discuss the properties of this novel approach and its design as well as limit of performance implications. The resulting design methodology is also illustrated by its application to a three-degree-of-freedom active vibration isolation system.