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Mathematics of Control, Signals, and Systems

, Volume 21, Issue 4, pp 303–336 | Cite as

A classification of generic families of control-affine systems and their bifurcations

  • Marek W. Rupniewski
  • Witold Respondek
Open Access
Original Article

Abstract

We study control-affine systems with n − 1 inputs evolving on an n-dimensional manifold for which the distribution spanned by the control vector fields is involutive and of constant rank (equivalently, they may be considered as 1-dimensional systems with n − 1 inputs entering nonlinearly). We provide a complete classification of such generic systems and their one-parameter families. We show that a generic family for n > 2 is equivalent (with respect to feedback or orbital feedback transformations) to one of nine canonical forms which differ from those for n = 2 by quadratic terms only. We also describe all generic bifurcations of 1-parameter families of systems of the above form.

Keywords

Feedback equivalence Bifurcation Control system 1-Parameter family Involutive distributions 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2010

Authors and Affiliations

  1. 1.Institute of Electronic SystemsWarsaw University of TechnologyWarsawPoland
  2. 2.Laboratoire de Mathématique EA3226INSA-RouenSaint-Etiennedu-RouvrayFrance

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