The Local Realization of Generating Series of Finite Lie Rank

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


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].


Constant Term Left Ideal Formal Power Series Formal Series Convergent Series 
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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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