Frequecy-weighted model reduction via interpolation
We propose a numerical method of the frequency-weighted model reduction. A model to be reduced (an original model) is a stable SISO discrete-time model which is 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 which chooses the interpolation points by searching in the unit circle to find the reduced-order model such that Lam,-norm of the reduction error is less than a prescribed value. This method has the following features, which shows 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 of finding the reduced-order model is simple and requires relatively a small amount of computation. iii) The order of the reduced-order model can be controlled by choosing the number of the interpolation points.