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# On $L_\infty$ Stabilization of Diagonal Semilinear Hyperbolic Systems by Saturated Boundary Control

2 GIPSA-INFINITY - GIPSA - Infinite Dimensional Dynamics
GIPSA-PAD - GIPSA Pôle Automatique et Diagnostic
Abstract : This paper considers a diagonal semilinear system of hyperbolic partial differential equations with positive and constant velocities coupled with a nonlinear source term. The boundary condition is composed of an unstable linear term and a saturated feedback control. Weak solutions with initial data in L 2 ([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.
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Cited literature [20 references]

https://hal.archives-ouvertes.fr/hal-02384422
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Submitted on : Monday, February 17, 2020 - 11:06:20 AM
Last modification on : Tuesday, April 5, 2022 - 3:40:29 AM
Long-term archiving on: : Monday, May 18, 2020 - 2:24:48 PM

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Mathias Dus, Francesco Ferrante, Christophe Prieur. On $L_\infty$ Stabilization of Diagonal Semilinear Hyperbolic Systems by Saturated Boundary Control. ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2020, 26 (23), pp.34. ⟨10.1051/cocv/2019069⟩. ⟨hal-02384422⟩

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