A two-variable approach to the model reduction problem with Hankel norm criterion

A two-variable approach to the model reduction problem with Hankel norm criterion is discussed. The problem is proved to be reducible to obtaining 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.