### Abstract

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 language | English (US) |
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Title of host publication | IFAC Symposia Series |

Publisher | Publ by Pergamon Press Inc |

Pages | 251-256 |

Number of pages | 6 |

Edition | 7 |

ISBN (Print) | 0080419011 |

State | Published - Jan 1 1993 |

Event | Proceedings of the IFAC Symposium on Nonlinear Control Systems Design 1992 - Bordeaux, Fr Duration: Jun 24 1992 → Jun 26 1992 |

### Publication series

Name | IFAC Symposia Series |
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Number | 7 |

ISSN (Print) | 0962-9505 |

### Other

Other | Proceedings of the IFAC Symposium on Nonlinear Control Systems Design 1992 |
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City | Bordeaux, Fr |

Period | 6/24/92 → 6/26/92 |

### ASJC Scopus subject areas

- Engineering(all)

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## Cite this

Kawski, M. (1993). Combinatorics of realizations of nilpotent control systems. In

*IFAC Symposia Series*(7 ed., pp. 251-256). (IFAC Symposia Series; No. 7). Publ by Pergamon Press Inc.