Regular Rational Matrix Functions with Prescribed Pole and Zero Structure

  • I. Gohberg
  • M. A. Kaashoek
Part of the Operator Theory: Advances and Applications book series (OT, volume 33)

Abstract

The problem to construct all regular rational matrix functions with a prescribed pole and zero structure is solved explicitly. Also the necessary and sufficient condition for the existence of a solution is derived. The proofs use an appropriate Möbius transformation to reduce the problem to the case when the functions are regular at infinity.

Keywords

Rational Matrix Admissible Pair Minimal System Inverse Spectral Problem Minimal Realization 
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.

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References

  1. [1]
    Ball, J.A., Cohen, N., Ran, A.C.M.: Inverse spectral problems for regular improper rational matrix functions, this volume.Google Scholar
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    Ball, J.A., Ran, A.C.M.: Global inverse spectral problems for rational matrix functions, Linear Algebra and Applications 86 (1987), 237–282.CrossRefGoogle Scholar
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    Ball, J.A., Ran, A.C.M.: Local inverse spectral problems for rational matrix functions, Integral Equations and Operator Theory 10 (1987), 349–415.CrossRefGoogle Scholar
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    Bart, H., Gohberg, I., Kaashoek, M.A.: Minimal factorization of matrix and operator functions, OT 1, Birkhäuser Verlag, Basel, 1979.Google Scholar
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    Gohberg, I., Kaashoek, M.A.: An inverse spectral problem for rational matrix functions and minimal divisibility, Integral Equations and Operator Theory 10 (1987), 437–465.CrossRefGoogle Scholar
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    Gohberg, I., Kaashoek, M.A., Lerer, L., Rodman, L.: Minimal divisors of rational matrix functions with prescribed zero and pole structure, in: Topics in Operator Theory, Systems and Networks (Eds. H. Dym and I. Gohberg), OT12, Birkhäuser Verlag, Basel, 1984, pp. 241–275.Google Scholar

Copyright information

© Springer Basel AG 1988

Authors and Affiliations

  • I. Gohberg
    • 1
  • M. A. Kaashoek
    • 2
  1. 1.Raymond and Beverly Sackler, Faculty of Exact Sciences, School of Mathematical SciencesTel-Aviv UniversityRamat-AvivIsrael
  2. 2.Department of Mathematics and Computer ScienceVrije UniversiteitAmsterdamThe Netherlands

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