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Mathematics of Control, Signals and Systems

, Volume 12, Issue 4, pp 361–375 | Cite as

Hankel Singular Values and Vectors of a Class of Infinite-Dimensional Systems: Exact Hamiltonian Formulas for Control and Approximation Problems

  • Yoshito Ohta

Abstract.

This paper derives exact formulas for singular values and vectors of Hankel operators whose symbol is a product of a single-input single-output inner function and a multi-input multi-output rational function. This class of Hankel operators arises from the sensitivity minimization H control problem with a rational weight function and the approximation problem of transfer functions having rational outer parts. It is shown that there is a Hamiltonian transcendental equation characterizing singular values which leads to a matrix function formula for singular vectors.

Key words. Hankel operator, Hankel singular value, Hankel singular vector, Model reduction, Infinite-dimensional systems, Inner function. 

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Copyright information

© Springer-Verlag London Limited 1999

Authors and Affiliations

  • Yoshito Ohta
    • 1
  1. 1.Department of Computer-Controlled Mechanical Systems, Osaka University, Suita, Osaka 565-0871, Japan. ohta@mech.eng.osaka-u.ac.jp.JP

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