New results on frequency weighted balanced reduction technique

In this paper, we show by an example that Enns frequency weighted balanced reduction procedure when applied to a scalar stable transfer function with input and output weights can result in an unstable reduced order model. A variation on the method is then presented which is guaranteed to yield stable reduced order models even when both input and output weightings are included. The method is a generalization of Lin and Chiu's technique and can handle weighting transfer functions which are proper rather than only strictly proper. A frequency response error bound for the proposed technique is also derived which is applicable for proper (including strictly proper) weighting functions.