Thesis of Danilo Rodrigues de lima

Nouveaux observateurs pour les systèmes dynamiques non-linéaires via la théorie de Lie avec des applications à la robotique

This thesis aims to introduce and study a class of continuous-time dynamical systems characterized by the existence of symmetries on the state, input and time. The concept of time symmetry can be encompassed by more general definitions found in the litterature, however their properties were never explored in generality through the lenses of dynamical anaysis and observer design, a shortcoming that this thesis adresses. Their importance is well justified due to their generalization of homogeneous systems and their display of exclusive features such as Finite-Time Stability. Examples of systems possessing symmetries are considered and studied for the purposes of observer and control design, namely an extended class of Persidskii systems and a Unycicle Mobile Robot.

Jury

Mme Rosane USHIROBIRA Directrice de recherche Inria, Lille Directrice de thèse, M. Silvère BONNABEL Professeur École des Mines Rapporteur, M. Vincent ANDRIEU Directeur de recherche CNRS U. Lyon Rapporteur, Mme Catherine BONNET Directrice de recherche Inria, Saclay Examinatrice, M. Antoine CHAILLET Professeur, CentraleSupélec Examinateur, M. Denis EFIMOV Directeur de recherche Inria, Lille Co-directeur de thèse.

Thesis of the team VALSE defended on 24/02/2026