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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