On frequency weighted balanced truncation technique retaining Hankel singular values

A modification to Lin and Chiu´s technique of frequency weighted balanced truncation is presented. The method is based on simultaneously diagonalizing the frequency weighted controllability and observability Gramians. Instead of obtaining the reduced order models from the truncated frequency weighted balanced realization as in the conventional techniques, the models are obtained from the truncated augmented system realizations which ensure matching of the dominant frequency weighted Hankel singular values. The method is compared with the method of using numerical examples.