On Model Reduction in System Identification

In this paper we will study how to use model reduction in system identification. We propose an identification algorithm based on the least squares identification method and either of the three model reduction techniques: Frequency weighted L² model reduction, model reduction via a frequency weighted balanced realization or frequency weighted optimal Hankel-norm model reduction. The frequency weighted L² model reduction is optimal in a minimum variance sense, while the advantage of the two other model reduction techniques is that a consistent identification algorithm with closed form solution is obtained.