On the Geometric Interpretation of the Polynomial Lie Bracket for Nonlinear Time-Delay Systems

Claudia Califano (1) , Stefano Battilotti (1) , Claude H. Moog (2)

1 DIAG UNIROMA - Dipartimento di Ingegneria informatica automatica e gestionale [Roma]
2 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes

Time–delay systems are infinite dimensional, thus standard differential geometric tools can not be applied in a straightforward way. Though, thanks to a suitable extended Lie Bracket – or Polynomial Lie Bracket – which has been introduced recently, it is still possible to build up a geometric framework to tackle the analysis and synthesis problems for nonlinear time delay systems. The major contribution herein is to show that those geometric generalizations are not just formal, but are interpreted in terms of successive forward and backward flows similarly to the Lie Bracket of delay free vector fields.

Mots clés: Time–delay systems; Lie bracket; geometric approach; nonlinear systems

Domaines: Automatique

Claudia Califano, Stefano Battilotti, Claude H. Moog. On the Geometric Interpretation of the Polynomial Lie Bracket for Nonlinear Time-Delay Systems. 55th IEEE Conference on Decision and Control, IEEE, Dec 2016, Las Vegas, United States. pp.555 - 560, ⟨10.1109/CDC.2016.7798327⟩. ⟨hal-01351911⟩