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

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Antoine Chaillet
Jakub Orłowski
Pierdomenico Pepe
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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.
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Dates and versions

hal-03114574 , version 1 (19-01-2021)

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  • HAL Id : hal-03114574 , version 1

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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), Dec 2019, Nice, France. ⟨hal-03114574⟩
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