| 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: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
2
October
2018
Accepted:
18
November
2019
Abstract
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
Research by F. Ferrante has been partially supported by the CNRS-INS2I under the JCJC grant CoBrA and by the Grenoble Institute of Technology under the grant CrYStAL.
© 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.
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