Factorization-based frequency-weighted optimal Hankel-norm model reduction

Abstract

In this paper, we present frequency-weighted optimal Hankel-norm model reduction algorithms for linear time-invariant continuous-time systems by representing an original higher-order system into new fictitious systems. The new system representations are derived through factorization of the resulting sub-matrices that are obtained after transformations. As the proposed approaches are factorization dependent, additional results with both approaches are included using another factorization of the fictitious input–output and weight matrices. The proposed algorithms generate stable reduced models with double-sided weights and provide a substantial improvement in the weighted error. A numerical example is given to compare the efficacy of the proposed algorithms with the well-known frequency-weighted techniques.