On the Existence of the Normal Form for Nonlinear Delay Systems

Claudia Califano (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

The normal form is discussed for nonlinear systems affected by constant commensurate delays. Two different forms are argued. In particular, necessary and sufficient conditions are given under which a nonlinear time-delay system can be decomposed into a (weakly) observable subsystem and a non observable subsystem. Whenever such a decomposition exists, additional conditions are required to ensure the feedback linearization of the weakly observable subsystem. Finally, a full characterization is derived for the nonlinear time delay system to have an unobservable subsystem not directly affected by the input and a weakly observable subsystem which is linearizable by feedback. The performed analysis is carried out within a new geometric framework recently introduced in the literature.

Domaines: Automatique

Claudia Califano, Claude H. Moog. On the Existence of the Normal Form for Nonlinear Delay Systems. Malisoff, M.; Pepe, P.; Mazenc, F.; Karafyllis, I. Recent Results on Nonlinear Delay Control Systems, 4, Springer, pp.113-142, 2016, Advances in Delays and Dynamics, 9783319180717. ⟨10.1007/978-3-319-18072-4_6⟩. ⟨hal-01179602⟩