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Frequency domain solution of the H problem for descriptor systems

  • Huibert Kwakernaak
Part D Robust Control
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 241)

Abstract

The standard H problem for descriptor systems is solved by frequency domain techniques relying on spectral factorization. An algorithm of Clements for the spectral factorization of rational matrices is adapted to the descriptor problem. It leads to a compact and efficient solution that involves transforming two suitable matrix pencils to Clements form.

Keywords

Descriptor System Imaginary Axis Rational Matrix Algebraic Riccati Equation Matrix Pencil 
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]
    J. D. Aplevich. Implicit linear systems, volume 152 of Lecture Notes in Control and Information Sciences. Springer-Verlag, Berlin, etc., 1991.zbMATHGoogle Scholar
  2. [2]
    D. J. Clements. Rational spectral factorization using state-space methods. Systems & Control Letters, 20:335–343, 1993.zbMATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    J. C. Doyle. Lecture Notes, ONR/Honeywell Workshop on Advances in Multivariable Control, Minneapolis, Minn., 1984.Google Scholar
  4. [4]
    J. C. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis. State-space solutions to standard H 2 and H control problems. IEEE Trans. Aut. Control, 34:831–847, 1989.zbMATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    G. M. Golub and C. Van Loan. Matrix Computations. The Johns Hopkins University Press, Baltimore, Maryland, 1983.zbMATHGoogle Scholar
  6. [6]
    H. Kwakernaak. Frequency domain solution of the standard H problem. In M. J. Grimble and V. Kučera, editor, Polynomial Methods for Control Systems Design, chapter 2, pages 1741–1746. Springer, London, etc., 1996.Google Scholar
  7. [7]
    H. Kwakernaak and M. Šebek. Polynomial J-spectral factorization. IEEE Trans. Aut. Control, 39(2):315–328, 1994.zbMATHCrossRefGoogle Scholar
  8. [8]
    J. W. Polderman and J. C. Willems. Introduction to mathematical systems theory — A behavioral approach. Springer, New York, etc., 1997.zbMATHGoogle Scholar
  9. [9]
    K. Takaba, N. Morihira, and T. Katayama. H Control for descriptor systems — A J-spectral factorization approach. In Proc. 33rd IEEE Conf. Decision & Control, pages 2251–2256, Lake Buena Vista, FL, 1994.Google Scholar
  10. [10]
    P. Van Dooren. A generalized eigenvalue approach for solving Riccati equations. SIAM J. Sci. Stat. Comput., 2(2):121–135, 1981.zbMATHCrossRefGoogle Scholar
  11. [11]
    G. C. Verghese, B. Lévy, and Th. Kailath. A generalized state-space for singular systems. IEEE Trans. Aut. Control, 26(4):811–831, 1981.zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 1999

Authors and Affiliations

  • Huibert Kwakernaak
    • 1
  1. 1.Systems and Control Group, Faculty of Applied MathematicsUniversity of TwenteEnschedeThe Netherlands

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