Volume 26, 2020
|Number of page(s)||34|
|Published online||02 March 2020|
On L∞ stabilization of diagonal semilinear hyperbolic systems by saturated boundary control*
Univ. Paul Sabatier, Institut de Mathématiques de Toulouse,
118 route de Narbonne,
Toulouse Cedex 9, France.
2 Univ. Grenoble Alpes, CNRS, Grenoble INP, GIPSA-lab, 38000 Grenoble, France.
** Corresponding author: firstname.lastname@example.org
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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