In this paper, a linear hyperbolic system of balance laws with boundary disturbances in one dimension is considered. An explicit candidate Input-to-State Stability (ISS)-Lyapunov function in \(L^2-\)norm is considered and discretised to investigate conditions for ISS of the discrete system as well. Finally, experimental results on test examples including the Saint-Venant equations with boundary disturbances are presented. The numerical results demonstrate the expected theoretical decay of the Lyapunov function.

中文翻译：

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通过边界反馈控制的非均匀线性双曲线平衡律系统的输入状态稳定性

本文考虑了一维带有边界干扰的平衡律线性双曲系统。考虑并离散化了\（L ^ 2- \）范数中的显式候选输入状态稳定性（ISS）-Lyapunov函数，并离散化该变量以研究离散系统的ISS条件。最后，给出了包括带边界扰动的Saint-Venant方程在内的测试示例的实验结果。数值结果证明了李雅普诺夫函数的预期理论衰减。