Quasi-generalized singular perturbation

The extension of the generalized singular perturbation (GSP) method proposed by Fernando and Nicholson (1982) to the frequency-weighting case is considered. Apart from two special cases of this technique, namely the balanced truncation (BT) and the balanced residualization (BR) methods which approximate the GSP at infinity and zero frequencies, respectively, reduced-order models produced by the GSP approach will have state-space matrices with complex elements. We propose a method that produces reduced-order models having state-space matrices with real elements, which preserve the characteristics of both BT and BR to a certain degree, according to a parameter chosen in the model-order reduction process