Skip to main content

Nehari interpolation problem for rational matrix functions: The generic case

Part of the Lecture Notes in Mathematics book series (LNMCIME,volume 1496)

Abstract

We study here a matrix Nehari problem, regarded as an interpolation problem, for the class of rational matrix functions. The interpolation data are assumed to be in a simple, but generic form. This allows us to present a self-contained exposition of the matrix Nehari problem, including criteria for solvability and description of all solutions. The proofs are based on the state-space method.

Keywords

  • Interpolation Problem
  • Hankel Operator
  • Interpolation Condition
  • Finite Rank Operator
  • Rational Matrix Function

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Partially supported by the NSF Grant DMS-8701615-02.

Partially supported by the NSF Grant DMS-9000839.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. V. M. Adamjan, D. Z. Arov and M. G. Krein, Infinite block Hankel matrices and their connection with the interpolation problem, Amer. Math. Soc. Transl.(2) 111(1978), 133–156; Russian original, 1971.

    Google Scholar 

  2. J. A. Ball, I. Gohberg and L. Rodman, Interpolation of Rational Matrix Functions, OT45, Birkhäuser, 1990.

    Google Scholar 

  3. J. A. Ball, I. Gohberg and L. Rodman, Tangential interpolation problems for rational matrix functions, Proc. Symposia in Applied Math 40(1990), 59–86.

    CrossRef  MathSciNet  Google Scholar 

  4. J. A. Ball, I. Gohberg and L. Rodman, Boundary Nevanlinna-Pick interpolation for rational matrix functions, preprint.

    Google Scholar 

  5. C. Foias and A. E. Frazho, The Communtant Lifting Approach to Interpolation Problems, OT44, Birkhäuser, 1990.

    Google Scholar 

  6. I. Gohberg (editor), I. Schur Methods in Operator Theory and Signal Processing, OT18, Birkhäuser, 1986.

    Google Scholar 

  7. K. Glover, All optimal Hankel-norm approximations of linear multivariable systems and their L error bounds, International J. Control 39(1984), 1115–1193.

    CrossRef  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ball, J.A., Gohberg, I., Rodman, L. (1991). Nehari interpolation problem for rational matrix functions: The generic case. In: Mosca, E., Pandolfi, L. (eds) H-Control Theory. Lecture Notes in Mathematics, vol 1496. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084472

Download citation

  • DOI: https://doi.org/10.1007/BFb0084472

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54949-9

  • Online ISBN: 978-3-540-46604-8

  • eBook Packages: Springer Book Archive