Pole placement and the observer-based controller parameterization

Two properties related to observer-based controller parameterization and pole placement are discussed. It is shown that the poles of the closed-loop system with observer-based controller parameterization can be classified into three groups, and each group of poles can be independently determined. These three groups of poles are the regulator poles, the observer poles, and the poles of the added dynamics. If the realization of the controller is not minimal, then the uncontrollable and/or unobservable controller poles can be removed and the order of the controller is minimized. The set of these removable controller poles is a subset of the regulator and the observer poles. The poles of the closed-loop system with the minimal order controller will include all the poles of a parameter matrix and some of the regulator and the observer poles which are not the removable controller poles