One-step extension approach to optimal Hankel-norm approximation and H^∞-optimization problems

This paper provides a novel methodology for Hankel approximation and H^∞-optimization problems, based on a new formulation of the one-step extension problem which was originally proposed by A-A-K and is solved here by the Sarason interpolation theorem. The parameterization of all optimal Hankel approximants for multivariable systems is given in terms of the eigenvalue decomposition of a Hermitian matrix composed directly from the coefficients of a given transfer function matrix φ. Rather than starting with the state-space realization of φ, we use polynomial coefficients of φ as input data. In terms of these data, a natural basis is given for the finite dimensional Sarason model space and all computations involve only manipulations with finite matrices.