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Article Dans Une Revue Systems and Control Letters Année : 2021

Global exponential stability and Input-to-State Stability of semilinear hyperbolic systems for the $L^{2}$ norm

Résumé

In this paper we study the global exponential stability in the $L^{2}$ norm of semilinear 1-d hyperbolic systems on a bounded domain, when the source term and the nonlinear boundary conditions are Lipschitz. We exhibit two sufficient stability conditions: an internal condition and a boundary condition. This result holds also when the source term is nonlocal. Finally, we show its robustness by extending it to global Input-to State Stability in the L 2 norm with respect to both interior and boundary disturbances.
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Dates et versions

hal-03018577 , version 1 (22-11-2020)

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Amaury Hayat. Global exponential stability and Input-to-State Stability of semilinear hyperbolic systems for the $L^{2}$ norm. Systems and Control Letters, 2021, pp.104848. ⟨10.1016/j.sysconle.2020.104848⟩. ⟨hal-03018577⟩
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