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

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