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

A methodology is presented for Hankel approximation and H ^∞-optimization problems that is based on a new formulation of a one-step extension problem which is solved by the Sarason interpolation theorem. The parameterization of all optimal Hankel approximants for multivariable systems is given in terms of the eigenvalue decomposition of an Hermitian matrix composed directly from the coefficients of a given transfer function matrix φ. Rather than starting with the state-space realization of φ, the authors 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