Frequency-weighted model reduction via interpolation

Abstract

We propose a numerical method of frequency-weighted model reduction. The model to be reduced (an original model) is a stable SISO discrete-time model described by high-order state-space equations. We design the reduced-order model so that it can interpolate 1st- and 2nd-order information of the original model at complex frequency points (interpolation points) in the unit circle. The characteristics of the reduced-order model greatly depend on the choice of the interpolation points. The proposed model reduction method is a numerical one that chooses the interpolation points by searching in the unit circle to find the reduced-order model such that L∞-norm of the reduction error is less than a prescribed value. This method has the following features that show that it is an effective numerical method of the frequency-weighted model reduction. i) The reduced-order model is guaranteed to be stable. ii) The procedure for finding the reduced-order model is simple and requires a relatively small amount of computation. iii) The order of the reduced-order model can be controlled by choosing the number of interpolation points. © 1998 Scripta Technica, Electr Eng Jpn, 126(2): 31–39, 1999