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Immersion in infinite dimension

  • Algebraic and Geometric System Theory
  • 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

The input-output map is the intrinsic object of a dynamical system. The immersion problem consists of sending a dynamical system to another one via a transformation which preserves the input-output maps.

Many authors have studied the immersion of nonlinear systems into a finite dimensional state affine systems (up to output injection).

This result can be applied to the synthesis of observers of nonlinear systems.

In this paper we prove that under some assumptions, any autonomous single output system can be immersed into an infinite dimensional linear system on some Banach space.

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References

  1. D. Bossane, D. Rakotopara, J.P. Gauthier: “Local and global immersion into linear systems up to output injection”. Submitted to M.C.S.S.

    Google Scholar 

  2. F. Celle, J.P. Gauthier, D. kasakos, G. Sallet: “Synthesis of nonlinear observers, a harmonic analysis approach”, Math. systems theory, vol. 22, pp 291–322.

    Google Scholar 

  3. M. Fliess, I. Kupka: “A finiteness creterion for nonlinear input-output differtial systems”, SIAM journal on control and opt. vol. 21 No 5, pp 721–728, Sep. 1983.

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  4. H. Hammouri, J.P. Gauthier: “Bilinearization up to output injection”, Systems and control letters 11, 1988, pp 139–149.

    Article  MATH  MathSciNet  Google Scholar 

  5. H. Hammouri, J.P. Gauthier: “The time varying linearization up to output injection”, 28th CDC, Tampa, Florida, Dec. 13–15 1989.

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  6. H. Hammouri, F. Celle, “Some results on nonlinear systems equivalence”, Joint conf. on new trends in systems theory, Genova, Italy, July 9–11, 1990.

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  7. A. J. Krener, A. Isidori: “Linearization by output injection and nonliear observers”, Systems and control letters 3, 1985, pp 47–52.

    Article  MathSciNet  Google Scholar 

  8. J. Levine, R. Marino: “Nonlinear systems immersion, observer and finite dimensional filters”, Systems and control letters 7, 1986, pp 133–142.

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Laboratoire d’Automatique et de Génie des Procédés, Université Claude Bernard Lyon I, 43 Bd de 11 Nov. 1918, 69622, Villeurbanne, France

    H. Hammouri & S. Othman

Authors
  1. H. Hammouri
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  2. S. Othman
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Editor information

A. Bensoussan J. L. Lions

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© 1990 Springer-Verlag

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Hammouri, H., Othman, S. (1990). Immersion in infinite dimension. 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/BFb0120062

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  • DOI: https://doi.org/10.1007/BFb0120062

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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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