Thesis: Analyse robuste des systèmes incertains descripteurs par des fonctions de Lyapunov non quadratiques

PhD defense: Ana Carolina DOS SANTOS PAULINA

Title: Analyse robuste des systèmes incertains descripteurs par des fonctions de Lyapunov non quadratiques

Team: AVR

Abstract: Uncertain descriptor systems are a convenient framework for simultaneously representing uncertainties in a model, as well as impulsive behavior and algebraic constraints. This is far beyond what can be depicted by standard dynamic systems, but it also means that the analysis of uncertain descriptor systems is more complex than the standard case. Research has been conducted to reduce the degree of conservatism in the analysis of uncertain descriptor systems. This can be achieved by using classes of Lyapunov functions that are known to be able to provide necessary and sufficient conditions for this evaluation. Homogeneous polynomial Lyapunov functions constitute one of such classes, but they have never been employed in the context of uncertain descriptor systems. In this thesis, we fill in this scientific gap, extending the use of homogeneous polynomial Lyapunov functions from the standard uncertain case for the uncertain descriptor one.

The jury is composed of Gabriela Iuliana BARA, Associate Professor at the university of Strasbourg, HDR (PhD director), Cristina MANIU, Associate Professor à CentraleSupélec, HDR (reviewer), Germain GARCIA, Professor at INSA Toulouse, HDR (reviewer),Rachid OUTBIB, Professor at the Aix-Marseille university, HDR (external member) and Edouard LAROCHE, Professor at the university of Strasbourg, HDR (external member).

The thesis defense, in French, take place on Wednesday, December 12 at 1:30 pm, in the amphitheater A302 at Télécom Physique Strasbourg.

Keywords: uncertain descriptor systems, nonquadratic Lyapunov functions, necessary and sufficient conditions, LMIs.