Causal observability of nonlinear time-delay systems with unknown inputs.

Gang Zheng (1, 2) , Jean-Pierre Null Barbot (1, 3) , Driss Boutat (4) , Thierry Floquet (1, 5) , Jean-Pierre Richard (1, 5)

1 ALIEN - Algebra for Digital Identification and Estimation
2 LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal
3 ECS-Lab - Électronique et Commande des Systèmes Laboratoire
4 PRISME - Laboratoire Pluridisciplinaire de Recherche en Ingénierie des Systèmes, Mécanique et Energétique
5 SyNeR - Systèmes Non Linéaires et à Retards

This paper investigates the problem of causal observability of the states and unknown inputs of nonlinear time-delay systems. Using the theory of non-commutative rings, the nonlinear time-delay system is transformed into a suitable canonical form to solve the problem. A necessary and sufficient condition is given to guarantee the existence of a change of coordinate leading to such a form. Then, algorithms are provided to check the possibility of obtaining causal estimations of the states and unknown inputs for the studied systems.

Mots clés: delay system; observability; nonlinear; observers with unknown inputs

Domaines: Automatique / Robotique; Automatique; Optimisation et contrôle [math.OC]

Gang Zheng, Jean-Pierre Null Barbot, Driss Boutat, Thierry Floquet, Jean-Pierre Richard. Causal observability of nonlinear time-delay systems with unknown inputs.. CDC'10, 49th IEEE Conf. on Decision & Control, Dec 2010, Atlanta, Georgia, United States. ⟨hal-00519504⟩