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A combinatorial approach of the nonlinear sampling problem

  • Control of Finite Dimensional Systems
  • Conference paper
  • First Online:
Analysis and Optimization of Systes

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 144))

Abstract

In this paper, results of combinatorial interest taken from the well-known Baker-Campbell-Hausdorff formula are proposed. They are used to analyze algebraic relations between nonlinear continuous time systems and their discretized analogues.

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References

  1. J.P. BARBOT, A computer aided design for sampling a nonlinear system in “Applied Algebra, Algebraic Algorithms and Error Correcting Codes, Lect. Notes in Comp. Sc. 357, T. Mora ed. pp. 74–88, 1989.

    Google Scholar 

  2. P. CROUCH, F. LAMNABHI-LAGARRIGUE, Algebraic and multiple integral identities, Acta Applicanda Mathematicae 15, pp 235–274, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  3. R. GOODMAN, Lifting vector fields to nilpotent Lie groups, J. Math. Pures & Appli., 57, pp. 77–86, (1978).

    MATH  Google Scholar 

  4. M. FLIESS, Fonctionnelles causales non linéaires et indéterminées non commutatives, Bull. Soc. Math. France, 109, pp. 3–40 1981.

    MATH  MathSciNet  Google Scholar 

  5. M. FLIESS and D. NORMAND-CYROT, Algèbres de Lie nilpotentes, formule de Baker-Campbell-Haussdorff et intégrales itérées de K.T. Chen, séminaire de probabilités, 1980–1981, 16, Lect. Notes in Math., J. Azema and M. Yor eds., pp. 257–267, Springer-Verlag, 1982.

    Google Scholar 

  6. P. LEROUX and X.G. VIENNOT, A combinatorial approach to nonlinear functional expansions: an introduction with an example, Proc 27-th IEEE-CDC, Austin Texas, USA, 1988.

    Google Scholar 

  7. S. MONACO and D. NORMAND-CYROT, On the sampling of a linear control system, Rap. 6–84, DIS, Rome, Proc. 24th IEEE CDC, Fort Lauderdale, USA, pp. 90–95, 1985.

    Google Scholar 

  8. S. MONACO and D. NORMAND-CYROT, Invariant distributions under sampling, Theory and Applications of Nonlinear Control Systems, (C.I. Byrnes and A. Linquist eds.) North Holland, pp. 215–221, 1986.

    Google Scholar 

  9. S. MONACO and D. NORMAND-CYROT, Zero dynamics of sampled nonlinear systems, Syst. and Contr. Letters, 11, pp. 229–234, 1989.

    Article  Google Scholar 

  10. S. MONACO and D. NORMAND-CYROT, Functional expansions for nonlinear discrete time systems, Mathematical Systems Theory 21, pp. 235–254 1989.

    Article  MATH  MathSciNet  Google Scholar 

  11. S. MONACO and D. NORMAND-CYROT, Combinatorial relations between discrete and continuous time nonlinear systems, submitted for publication, 1990.

    Google Scholar 

  12. R. REE, Lie elements and an algebra of shuffles, Ann. of Math., 68, pp. 210–220, 1958.

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica e Sistemistica, Università di Roma, “La Sapienza”, Via Eudossiana 18, 00184, Rome, Italy

    S. Monaco

  2. Laboratoire des Signaux & Systèmes, CNRS-ESE, Plateau de Moulon, 91192, Gif-sur-Yvette Cedex, France

    D. Normand-Cyrot

Authors
  1. S. Monaco
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  2. D. Normand-Cyrot
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Editor information

A. Bensoussan J. L. Lions

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© 1990 Springer-Verlag

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Monaco, S., Normand-Cyrot, D. (1990). A combinatorial approach of the nonlinear sampling problem. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systes. Lecture Notes in Control and Information Sciences, vol 144. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120100

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  • DOI: https://doi.org/10.1007/BFb0120100

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52630-8

  • Online ISBN: 978-3-540-47085-4

  • eBook Packages: Springer Book Archive

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