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

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.