A relaxed Lyapunov-Krasovskii condition for global exponential stability of Lipschitz time-delay systems

Antoine Chaillet (1) , Jakub Orłowski (1) , Pierdomenico Pepe (2)

1 L2S - Laboratoire des signaux et systèmes
2 UNIVAQ - University of L'Aquila [Italy]

For nonlinear time-delay systems with globally Lipschitz vector fields, we propose a relaxed sufficient condition for global exponential stability (GES), in which the dissipation rate of the Lyapunov-Krasovskii functional is not needed to involve the functional itself, but merely the point-wise current value of the solution. Our proof technique consists in explicitly constructing a Lyapunov-Krasovskii functional that satisfies existing criteria for GES. Consequences for robustness to exogenous inputs are briefly evoked and an example taken from neuroscience literature illustrates the applicability of the result.

Domaines: Automatique / Robotique

Antoine Chaillet, Jakub Orłowski, Pierdomenico Pepe. A relaxed Lyapunov-Krasovskii condition for global exponential stability of Lipschitz time-delay systems. 58th IEEE Conference on Decision and Control (CDC 2019), Dec 2019, Nice, France. ⟨10.1109/cdc40024.2019.9030092⟩. ⟨hal-03114574⟩