Combinatorics of realizations of nilpotent control systems

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations


This article gives a very simple algorithm which allows to immediately write down a canonical nonlinear representation of a free nilpotent Lie algebra. Specifically, it defines a set of local coordinates and gives a formula for the components of a set of system vector fields in terms of these coordinates. The components of iterated Lie brackets of the system vector fields can also be read off easily without any further differentiation. The formulae given here are very close to Sussmann's product expansion of the Chen-Fliess series and to the chronological calculus introduced by Agrachev and Gamkrelidze.

Original languageEnglish (US)
Title of host publicationIFAC Symposia Series
PublisherPubl by Pergamon Press Inc
Number of pages6
ISBN (Print)0080419011, 9780080419015
StatePublished - 1993
EventProceedings of the IFAC Symposium on Nonlinear Control Systems Design 1992 - Bordeaux, Fr
Duration: Jun 24 1992Jun 26 1992

Publication series

NameIFAC Symposia Series
ISSN (Print)0962-9505


OtherProceedings of the IFAC Symposium on Nonlinear Control Systems Design 1992
CityBordeaux, Fr

ASJC Scopus subject areas

  • Engineering(all)


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