Numerical approach for the frequency-weighted Hankel-norm approximation

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 software. We also discuss the solution of the frequency-weighted L_∞-norm model reduction problem and indicate how to solve it in the most general setting.