Numerical Approach for the Frequency-Weighted Hankel-Norm Approximation

Abstract

We derive new projection formulas for the model reduction method based on the frequency-weighted Hankel norm approximation (FWHNA). These formulas extend the applicability of the FWHNA method to frequency weights expressed as antistable right/left invertible rational matrices. By computing the projections via the solution of appropriate generalized Sylvester equations, an inversion-free solution of the FWHNA problem is possible. The new projection formulas allows to implement efficiently the FWHNA method as robust numerical L-infinity-norm model reduction problem and indicate how to solve it in the most general setting.