An improved frequency weighted balancing related technique with error bounds

In this paper, we present an improved frequency weighted balanced related technique which is based on a combination of the unweighted balanced technique (Moore, 1981; Liu and Anderson, 1989) with Lin and Chiu´s frequency weighted balanced Technique (Lin and Chiu, 1992). The reduced order models which are guaranteed to be stable in case of double-sided weighting, are obtained by either direct truncation or singular perturbation approximation. A simple, elegant and easily calculatable a priori error bounds are also derived. A numerical example and comparison with other well-known techniques show the effectiveness of the proposed technique.