A Tutorial on Hankel-Norm Approximation

A self-contained derivation is presented of the characterization of all optimal Hankel-norm approximations to a given matrix-valued transfer function. The approach involves a state-space characterization of all-pass systems as in the author’s previous work, but has been greatly simplified. A section of preliminary results is included giving general results on linear fractional transformations, Hankel operators and all-pass systems. These results then can be applied to give the characterization of all optimal Hankel-norm approximations of a given stable transfer function. Frequency response bounds for these approximations are then derived from finite rank perturbation results.