Rational approximations with Hankel-norm criterion

Abstract

A two-variable approach to the model, reduction problem with Hankel norm criterion is discussed. The problem is proved to be reducible to obtain a two-variable all-pass rational function, interpolating a set of parametric values at specified points inside the unit circle. A polynomial formulation and the properties of the optimal Hankel norm approximations are then shown to result directly from the general form of the solution of the interpolation problem considered. As a consequence, the recursive Nevanlinna algorithm can be employed and the essential stability properties of the solution can be established with the help of the Nevanlinna matrix [9]. This short paper is meant to briefly summarize the work in the full paper [8], where the reader is referred to for more details.