An efficient algorithm on optimal Hankel-norm approximation formultivariable systems

This note provides a novel methodology for Hankel approximation and H^∞-optimization problems, based on a new formulation of the one-step extension problem, which is solved by the Sarason interpolation theorem. The present method does not require an initial balanced realization, and the parameterization of all optimal solutions is given in terms of the eigenvalue decomposition of a Hermitian matrix composed directly from the coefficients of the given transfer function matrix