English

The zero dynamics of feedback linearisation and Ehresmann connections

Optimization and Control 2016-06-13 v1

Abstract

The notion of zero dynamics is a cornerstone of many solutions to important control problems such as feedback linearisation and disturbance decoupling. For a SISO affine control system with relative degree strictly less than the order of the system, it is known that there exists a state transformation and a feedback transformation such that the system can be transformed to a linear system. Making use of the fibre bundle structure induced by the state transformation we show that it is possible to define a connection on the state manifold such that the zero dynamics can be defined as a vertical vector field. In this formalism the zero dynamics can be understood as motions along the fibres of a fibre bundle.

Cite

@article{arxiv.1606.03327,
  title  = {The zero dynamics of feedback linearisation and Ehresmann connections},
  author = {Tinashe Chingozha and Otis T Nyandoro and Anton van Wyk and John E. D Ekoru},
  journal= {arXiv preprint arXiv:1606.03327},
  year   = {2016}
}
R2 v1 2026-06-22T14:22:33.526Z