Frequency weighted balanced reduction technique: a generalization and an error bound

In this paper, a new frequency weighted balanced reduction technique is presented. The method is guaranteed to yield stable reduced order models and is applicable to both discrete and continuous systems. It is a simple generalization of Al-Saggaf and Franklin's technique (1986, 1988), but can handle square double-sided weighting matrices, and requires no restriction relating input, state and output dimensions of the weight. A frequency-domain interpretation and a frequency response error bound for the proposed technique are also provided.