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In this paper, a linear hyperbolic system of balance laws with boundarydisturbances in one dimension is considered. An explicit candidateInput-to-State Stability (ISS)-Lyapunov function in $ L^2- $norm is consideredand discretised to investigate conditions for ISS of the discrete system aswell. Finally, experimental results on test examples including the Saint-Venantequations with boundary disturbances are presented. The numerical resultsdemonstrate the expected theoretical decay of the Lyapunov function.

An analysis of the input-to-state-stabilisation of linear hyperbolic systems of balance laws with boundary disturbances