| 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
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