A generalized entropy criterion for Nevanlinna - Pick interpolation with degree constraint

Christopher I. Byrnes, Tryphon T. Georgiou, Anders Lindquist

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Abstract

In this paper, we present a generalized entropy criterion for solving the rational Nevanlinna - Pick problem for n + 1 interpolating conditions and the degree of interpolants bounded by n. The primal problem of maximizing this entropy gain has a very well-behaved dual problem. This dual is a convex optimization problem in a finite-dimensional space and gives rise to an algorithm for finding all interpolants which are positive real and rational of degree at most n. The criterion requires a selection of a monic Schur polynomial of degree n. It follows that this class of monic polynomials completely parameterizes all such rational interpolants, and it therefore provides a set of design parameters for specifying such interpolants. The algorithm is implemented in state-space form and applied to several illustrative problems in systems and control, namely sensitivity minimization, maximal power transfer and spectral estimation.

Original languageEnglish (US)
Pages (from-to)822-839
Number of pages18
JournalIEEE Transactions on Automatic Control
Volume46
Issue number6
DOIs
StatePublished - Jun 1 2001

Keywords

  • Duality
  • Entropy
  • Interpolation
  • Power transmission
  • Robust control
  • Spectral estimation

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