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Article Dans Une Revue ESAIM: Control, Optimisation and Calculus of Variations Année : 2020

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

Résumé

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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Dates et versions

hal-02384422 , version 1 (17-02-2020)

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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, 2020, 26 (23), pp.34. ⟨10.1051/cocv/2019069⟩. ⟨hal-02384422⟩
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