Frequency weighted identification and model reduction via extended impulse response Gramian

Abstract

A method is presented for identification and model reduction of frequency weighted linear discrete time invariant systems. The method is an extension of the method proposed by Ang et al . (1995), which is based on the extended impulse response Gramian (EIRG). A weighting matrix formed from the impulse response of the frequency weighting is used to weight the EIRG of the original system. The identified/reduced-order models are obtained via singular value decomposition of the frequency weighted EIRG and are shown to converge to a frequency weighted balanced realization under certain conditions. An example is presented to illustrate the proposed method.