Directional interpolation via all-pass transfer function matrices and its application in Hankel-norm approximations

A new approach to the problem of multivariable interpolation via all-pass transfer function matrices that are not necessarily stable is presented. The approach applies to both state-space and classical function theoretic arguments and obtains a very simple expression for the all-pass matrix that satisfies the interpolation requirement. Unlike the solution that is obtained by the generalized Nevanlinna-Pick algorithm, this expression is derived in closed form explicitly in terms of the interpolation parameters. It allows a detailed investigation of the structure of the all-pass solution, and it is readily used in Hankel-norm approximations of linear multivariable systems