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
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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Submitted on : Tuesday, August 14, 2018 - 5:33:47 PM
Last modification on : Friday, January 10, 2020 - 9:10:08 PM
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  • HAL Id : hal-01857265, version 1
  • ARXIV : 1808.05370


Swann Marx, Yacine Chitour, Christophe Prieur. Stability analysis of dissipative systems subject to nonlinear damping via Lyapunov techniques. 2018. ⟨hal-01857265v1⟩



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