Advertisement

Pole Placement, Internal Stabilization and Interpolation Conditions for Rational Matrix Functions: A Grassmannian Formulation

  • Joseph A. Ball
  • Joachim Rosenthal
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 62)

Abstract

The problem of pole placement via dynamic feedback and the bitangential interpolation problem are shown to be both particular instances of a general subspace interpolation problem formulated for rational curves from projective space into a Grass-mannian manifold. The problem of determining the minimal degree d for an interpolant in terms of the problem data is shown to be computable via intersection theory in projective space. Using the projective dimension theorem bounds for the minimal degree interpolant curve are given.

Key words

Multivariable Systems Interpolation Problems Dynamic Feedback Compensation Autoregressive Systems 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    A.C. Antoulas, J.A. Ball J. Kang(Kim) and J.C. Willems, On the solution of the minimal interpolation problem, Linear Alg. and Appl., 137/138 (1990), 511–573.MathSciNetGoogle Scholar
  2. [2]
    A.C. Antoulas and J.C. Willems, A basis-free approach to linear exact modeling, preprint.Google Scholar
  3. [3]
    J.A. Ball and J.W. Helton, Lie groups over the field of rational functions, signed spectral factorization, signed interpolation and amplifier design, J. Operator Theory, 9 (1982), 1964.Google Scholar
  4. [4]
    J.A. Ball, I. Gohberg and L. Rodman, Interpolation of Rational Matrix Functions, Birkhäuser-Verlag, Basel-Berlin-Boston, 1990.zbMATHGoogle Scholar
  5. [5]
    J.A. Ball, I. Gohberg and L. Rodman, “Sensitivity minimization and bitangential Nevanlinna-Pick interpolation in contour integral form,” in Signal Processing II: Control Theory and Applications (ed. F.A. Grünbaum et al), IMA Vol. in Math, and its Appl. Vol. 23, Springer-Verlag, (1990), pp. 3–35.Google Scholar

Copyright information

© Springer-Verlag New York, Inc. 1994

Authors and Affiliations

  • Joseph A. Ball
    • 1
  • Joachim Rosenthal
    • 2
  1. 1.Department of MathematicsVirginia TechBlacksburgUSA
  2. 2.Department of MathematicsUniversity of Notre DameNotre DameUSA

Personalised recommendations