Extended Lie Brackets for Nonlinear Time-Delay Systems

Claudia Califano (1) , Luis-Alejandro Marquez Martinez (2) , Claude H. Moog (3)

1 DIS - Dipartimento di Informatica e Sistemistica "Antonio Ruberti"
2 CICESE - Centro de Investigacion Cientifica y de Education Superior de Ensenada [Mexico]
3 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes

The Extended Lie bracket operator is introduced for the analysis and control of nonlinear time-delay systems. This tool is used to characterize the integrability conditions of a given submodule. The obtained results have two fundamental outcomes. First, they define the necessary and sufficient conditions under which a given set of nonlinear one-forms in the n-dimensional delayed variables x(t),..., x(t-sD) where D is constant, are integrable. Secondly, they set the basis for the extension to this context of the geometric approach used for delay-free systems.

Mots clés: Delay systems; geometric approach; linear equivalence; nonlinear systems

Domaines: Automatique

Claudia Califano, Luis-Alejandro Marquez Martinez, Claude H. Moog. Extended Lie Brackets for Nonlinear Time-Delay Systems. IEEE Transactions on Automatic Control, 2011, 56 (9), pp.2213-2218. ⟨10.1109/TAC.2011.2157405⟩. ⟨hal-00625401⟩