Finite-time and asymptotic left inversion of nonlinear time-delay systems

Zohra Kader (1, 2) , Gang Zheng (3, 2) , Jean-Pierre Barbot (4, 5)

1 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
2 NON-A-POST - Non-Asymptotic estimation for online systems
3 DEFROST - Deformable Robots Simulation Team
4 ECS - Equipe Commande des Systèmes
5 QUARTZ - Laboratoire QUARTZ

In this paper we investigate the left invertibility problem for a class of nonlinear time-delay systems. In both cases of time delay systems with and without internal dynamics the invertibility conditions are given. A new approach based on the use of higher order sliding mode observer is developed for finite-time left invertibility and for asymptotic left inversion. Causal and non-causal estimation of the unknown inputs are respectively discussed. The results are illustrated by numerical examples in order to show the efficiency of the method and its limits.

Mots clés: Left inversion; nonlinear time-delay system; nonlinear system; internal dynamics; asymptotic left inversion

Domaines: Automatique; Automatique / Robotique

Zohra Kader, Gang Zheng, Jean-Pierre Barbot. Finite-time and asymptotic left inversion of nonlinear time-delay systems. Automatica, 2018, 95, pp.283-292. ⟨10.1016/j.automatica.2018.05.002⟩. ⟨hal-01781561⟩