Output frequency weighted balanced realization like controller order reduction

In this paper, an output frequency-weighted controller reduction is considered, and the reasons for reducing the controller order with such a setting are based on maintenance of stability and approximation of the original transfer function matrix considerations. We show how to modify the input-normal realization to allow for such an output frequency weighting, and an L^∞-norm bound on the weighted reduction error is derived. An example is also given to demonstrate the proposed method. The technique is applicable for both discrete- and continuous-time systems.