Bessel inequality for robust stability analysis of time-delay system

Frédéric Gouaisbaut (1) , Yassine Ariba (2) , Alexandre Seuret (1)

1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
2 LAAS - Laboratoire d'analyse et d'architecture des systèmes

This paper addresses the problem of the stability analysis for a linear time-delay systems via a robust analysis approach and especially the quadratic separation framework. To this end, we use the Bessel inequality for building operators that depend on the delay. They not only allow us to model the system as an uncertain feedback system but also to control the accuracy of the approximations made. Then, a set of LMIs conditions are proposed which tends on examples to the analytical bounds for both delay dependent stability and delay range stability.

Domaines: Automatique

Frédéric Gouaisbaut, Yassine Ariba, Alexandre Seuret. Bessel inequality for robust stability analysis of time-delay system. IEEE Conference on Decision and Control, Florence : Italie (2013), Dec 2013, Florence, Italy. pp.6. ⟨hal-00860375⟩