Directional Interpolation Via All-Pass Transfer Function Matrices and Its Application in Hankel-Norm Approximations

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Abstract

A new approach to the problem of multivariable interpolation via all-pass transfer function matrices that are not necessarily stable is presented. It applies both state-space and classical function theoretic arguments and it 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.

Original languageEnglish
Pages (from-to)1167-1170
Number of pages4
JournalIEEE Transactions on Automatic Control
Volume35
Issue number10
DOIs
StatePublished - Oct 1990

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