MINES ParisTech CAS - Centre automatique et systèmes

Necessary and sufficient stability conditions for time-delay systems

Date : 15/09/2022 De 16h00 à 17h00

Mathieu Bajodek, CentraleSupelec, Paris, France

This talk deals with stability analysis of time-delay systems. Is it possible to extend linear finite-dimensional conditions, issued from Laplace-domain or time-domain analysis, to linear infinite-dimensional systems ? The answer is yes but we can wonder if such conditions can be implemented numerically. The main objective is to propose numerical criteria of stability, which can be implemented in a fast and tractable way. For the case of time-delay systems, using the Legendre polynomials approximation and keeping track of the truncated error, necessary and sufficient stability conditions are proposed. The conservatism involved by the approximated order is also quantified and an estimation of the necessary and sufficient order for which the test has to be performed is provided.

M. Bajodek was born in Toulouse, in July 1995. In 2019, he received the "Diplôme de l''Ecole Normale Supérieure Paris-Saclay'' and the Master’s Degree from "Université Paris-Saclay'' in automatic control, signal and image processing. From 2019 to 2022, he was a Ph.D. student supervised by Alexandre Seuret and Frédéric Gouaisbaut at "Laboratoire d’Architecture et d’Analyse des Systèmes'' (LAAS) and worked on the stability analysis of ODE-PDE interconnected systems. In July 2022, he received the Ph.D. degree from "Université Paul Sabatier Toulouse III". He is currently starting a one-year postdoctoral position at CentraleSupelec with Hugo Lhachemi and Giorgio Valmorbida.