Converse Lyapunov-Krasovskii theorems for uncertain retarded differential equations

Ihab Haidar (1) , Paolo Mason (1) , Mario Sigalotti (2, 3)

1 L2S - Laboratoire des signaux et systèmes
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
3 GECO - Geometric Control Design

In this article we give a collection of converse Lyapunov–Krasovskii theorems for uncertain retarded differential equations. We show that the existence of a weakly-degenerate Lyapunov–Krasovskii functional is a necessary and sufficient condition for the global exponential stability of linear retarded functional differential equations. This is carried out using a switched system representation approach.

Mots clés: converse Lyapunov theorems; exponential stability; Time-delay system; switched systems; Lyapunov–Krasovskii functional

Domaines: Optimisation et contrôle [math.OC]

Ihab Haidar, Paolo Mason, Mario Sigalotti. Converse Lyapunov-Krasovskii theorems for uncertain retarded differential equations. Automatica, 2015, 62, pp.263-273. ⟨10.1016/j.automatica.2015.09.034⟩. ⟨hal-00924252v3⟩