Performance preserving controller reduction via additive perturbation of the closed-loop transfer function

In this note, a new performance preserving controller order reduction method is proposed. Here performance preservation indicates that the norm bound of the closed loop transfer function with reduced-order controller is not greater than the norm bound of the closed loop transfer function with full order controller. We assume additive perturbations to the closed-loop transfer function and obtain a sufficient condition for performance preservation. Two kinds of useful weightings are derived, and the controller reduction problem is solved via a frequency weighted model reduction problem.