New Approximants for Nonlinear Functional Expansions

  • Françoise Lamnabhi-Lagarrigue
  • Zerong Yu
Part of the Progress in Systems and Control Theory book series (PSCT, volume 7)

Abstract

This work is a first step in obtaining new approximations for nonlinear functional expansions which are realized by bilinear systems. They are derived from formal approximants obtained from a combinatorial theory introduced by Leroux and Viennot. They were successive truncations of a nonlinear continued fraction and may be seen as the analogue of Padé approximants for analytic functions. These new approximations should provide a better analysis of nonlinear systems than the use of Volterra series.

Keywords

Manifold 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    P. d’ALESSANDRO, A. ISIDORI and A. RUBERTI, Realization and structure theory of bilinear dynamical systems, SIAM J. Contr. Optim., 12, pp. 517–535.Google Scholar
  2. [2]
    P. FLAJOLET, Combinatorial aspects of continued fractions, Discrete Maths, 32, pp.125–161, 1980.Google Scholar
  3. [3]
    M. FLIESS, Fonctionnelles causales non linéaires et ind6terminees non commutatives, Bull Soc. Math. France, 109, pp. 3–40, 1981.Google Scholar
  4. [4]
    M FLIESS, M. LAMNABHI and F. LAMNABHI-LAGARRIGUE, An algebraic approach to nonlinear functional expansions, IEEE Trans. Circuits and Syst, 30, pp. 554–570,1982.CrossRefGoogle Scholar
  5. [5]
    C. HESPEL and G. JACOB, Approximation of nonlinear systems by bilinear ones, in “Algebraic and geometric methods in nonlionear control theory” (M. Fliess and M. Hazewinkel, Eds.), 1986.Google Scholar
  6. [6]
    M. LAMNABHI, Functional analysis of nonlinear electronic circuits, thèse d’Etat, Univ. Paris XI, 1986.Google Scholar
  7. [7]
    F. LAMNABHI-LAGARRIGUE, P. LEROUX and X. VIENNOT, Consolidated expansions of Volterra series by bilinear systems, in “Analyse des Systèmes Dynamiques Controles”,Lyon 1990.Google Scholar
  8. [8]
    P. LEROUX and X. VIENNOT, “A combinatorial approach to nonlinear functional expansions, 27th Conf. on Decision and Control”, Austin, Texas, 1988.Google Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Françoise Lamnabhi-Lagarrigue
    • 1
  • Zerong Yu
    • 1
  1. 1.Laboratoire des Signaux et SystèmesSUPELECGif-sur-Yvette CedexFrance

Personalised recommendations