Frequency weighted identification and model reduction via extended impulse response Gramian

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.