Issue |
ESAIM: COCV
Volume 26, 2020
|
|
---|---|---|
Article Number | 23 | |
Number of page(s) | 34 | |
DOI | https://doi.org/10.1051/cocv/2019069 | |
Published online | 02 March 2020 |
On L∞ stabilization of diagonal semilinear hyperbolic systems by saturated boundary control*
1
Univ. Paul Sabatier, Institut de Mathématiques de Toulouse,
118 route de Narbonne,
31062
Toulouse Cedex 9, France.
2
Univ. Grenoble Alpes, CNRS, Grenoble INP, GIPSA-lab,
38000
Grenoble, France.
** Corresponding author: christophe.prieur@gipsa-lab.fr
Received:
2
October
2018
Accepted:
18
November
2019
This paper considers a diagonal semilinear system of hyperbolic partial differential equations with positive and constant velocities. The boundary condition is composed of an unstable linear term and a saturated feedback control. Weak solutions with initial data in L2([0, 1]) are considered and well-posedness of the system is proven using nonlinear semigroup techniques. Local L∞ exponential stability is tackled by a Lyapunov analysis and convergence of semigroups. Moreover, an explicit estimation of the region of attraction is given.
Mathematics Subject Classification: 93D05 / 93D15 / 93D20
Key words: Diagonal semilinear hyperbolic systems / saturation / Lyapunov theory
© The authors. Published by EDP Sciences, SMAI 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.