Stability analysis of a 1D wave equation with a nonmonotone distributed damping

Swann Marx 1 Yacine Chitour 2 Christophe Prieur 3
1 LAAS - Laboratoire d'analyse et d'architecture des systèmes
2 L2S - Laboratoire des signaux et systèmes
3 GIPSA-SYSCO - SYSCO
GIPSA-DA - Département Automatique
Abstract : This paper is concerned with the asymptotic stability analysis of a one dimensional wave equation subject to a nonmonotone distributed damping. A well-posedness result is provided together with a precise characterization of the asymptotic behavior of the trajectories of the system under consideration. The well-posedness is proved in the nonstandard L p functional spaces, with p ∈ [2, ∞], and relies mostly on some results collected in Haraux (2009). The asymptotic behavior analysis is based on an attractivity result on a specific infinite-dimensional linear time-variant system.
Keywords : nonlinear control Lyapunov functionals 1D wave equation
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Conference papers
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https://hal.laas.fr/hal-02006292
Contributor : Swann Marx <>
Submitted on : Tuesday, February 5, 2019 - 10:43:14 AM
Last modification on : Friday, January 10, 2020 - 9:08:10 PM
Long-term archiving on: Monday, May 6, 2019 - 1:41:13 PM

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  • HAL Id : hal-02006292, version 1
  • ARXIV : 1902.02050

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Swann Marx, Yacine Chitour, Christophe Prieur. Stability analysis of a 1D wave equation with a nonmonotone distributed damping. Joint 8th IFAC Symposium on Mechatronic Systems (MECHATRONICS'19) and 11th IFAC Symposium on Nonlinear Control Systems (NOLCOS'19), Vienna, Austria, 2019., Sep 2019, Vienne, Austria. ⟨hal-02006292⟩

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