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The Local Realization of Generating Series of Finite Lie Rank

  • Christophe Reutenauer
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 29)

Abstract

Realization of nonlinear systems by state-space is a classical problem in control theory. This problem has been completely solved by Kaiman [10] in the case of linear systems. Similarly, it was solved for bilinear systems (see Brockett [2], d’Alessandro, Isidori, Ruberti [1], Fliess [3], Sussmann [12]). In the general case, let us mention the work of Sussmann [13], Hermann, Krener [7] and Jakubczyk [9]: they assume that the solutions are regular at any time and for any inputs. This restriction lead Fliess to study local realization of nonlinear systems [5].

Keywords

Constant Term Left Ideal Formal Power Series Formal Series Convergent Series 
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

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Copyright information

© D. Reidel Publishing Company 1986

Authors and Affiliations

  • Christophe Reutenauer
    • 1
    • 2
  1. 1.Université du Québec à Montréal and CNRSParisFrance
  2. 2.Département de Mathématiques d’InformatiqueUniversité du Québec à MontréalMontréalCanada

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