A Relaxed Lyapunov-Krasovskii Condition for Global Exponential Stability of Lipschitz Time-Delay Systems

Antoine Chaillet1, Jakub Orlowski2, Pierdomenico Pepe3

  • 1CentraleSupélec
  • 2CentraleSupélec, Université Paris-Saclay
  • 3University of L' Aquila

Details

10:20 - 10:40 | Wed 11 Dec | Méditerranée 2 | WeA02.2

Session: Delay Systems I

Abstract

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.