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

Swann Marx; Yacine Chitour; Christophe Prieur

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 [Toulouse]

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 : 1D wave equation Lyapunov functionals nonlinear control

Document type :

Conference papers

Domain :

Mathematics [math] / Analysis of PDEs [math.AP]

Computer Science [cs] / Automatic Control Engineering

Mathematics [math] / Optimization and Control [math.OC]

Complete list of metadatas

https://hal.laas.fr/hal-02006292
Contributor : Swann Marx <>
Submitted on : Tuesday, February 5, 2019 - 10:43:14 AM
Last modification on : Friday, October 11, 2019 - 8:22:08 PM
Long-term archiving on : Monday, May 6, 2019 - 1:41:13 PM

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

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

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