Rational Approximations with Hankel-Norm Criterion

Abstract

A two-variable approach to the model reduction problem with Hankel- norm criterion is discussed in this reprint. 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. Reprints. (KR)

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1980
Accession Number
ADA215217

Entities

People

  • S. Kung
  • Y. Genin

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Contracts
  • Decomposition
  • Eigenvalues
  • Electrical Engineering
  • Engineering
  • Equations
  • Interpolation
  • Linear Systems
  • Polynomials
  • Rational Functions
  • Transfer Functions
  • Universities

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Approximation Theory.
  • Systems Analysis and Design