Stability analysis of dissipative systems subject to nonlinear damping via Lyapunov techniques

Swann Marx 1 Yacine Chitour 2 Christophe Prieur 3
1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes [Toulouse]
3 GIPSA-SYSCO - SYSCO
GIPSA-DA - Département Automatique
Abstract : In this article, we provide a general strategy based on Lyapunov functionals to analyse global asymptotic stability of linear infinite-dimensional systems subject to nonlinear dampings under the assumption that the origin of the system is globally asymp-totically stable with a linear damping. To do so, we first characterize, in terms of Lyapunov functionals, several types of asymptotic stability for linear infinite-dimensional systems, namely the exponential and the polynomial stability. Then, we derive a Lyapunov functional for the nonlinear system, which is the sum of a Lyapunov functional coming from the linear system and another term with compensates the nonlinearity. Our results are then applied to the linearized Korteweg-de Vries equation and some wave equations.
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https://hal.laas.fr/hal-01857265
Contributor : Swann Marx <>
Submitted on : Friday, September 14, 2018 - 1:09:47 PM
Last modification on : Thursday, August 22, 2019 - 11:32:03 AM
Long-term archiving on : Saturday, December 15, 2018 - 12:38:42 PM

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  • HAL Id : hal-01857265, version 2
  • ARXIV : 1808.05370

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Swann Marx, Yacine Chitour, Christophe Prieur. Stability analysis of dissipative systems subject to nonlinear damping via Lyapunov techniques. European Control Conference (ECC 2018), Jun 2018, Limassol, Cyprus. ⟨hal-01857265v2⟩

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