具有非局部速度的标量守恒律的输入-状态稳定性
Input-to-state stability of a scalar conservation law with nonlocal velocity
摘要：
本文研究了具有非局部速度和测量误差的标量守恒律平衡点在高度重入制造系统中的输入-状态稳定性。利用适当的李雅普诺夫函数，证明了ISS的充分必要条件必要条件.我们还分析了具有非局部速度和测量误差的离散标量守恒律的ISS的数值离散化。一个合适的离散化的李雅普诺夫函数也进行了分析，以提供数值逼近的平衡ISS。最后，我们展示了数值模拟，以验证理论研究结果。
英文摘要：
In this paper, we study input-to-state stability (ISS) of an equilibrium for a scalar conservation law with nonlocal velocity and measurement error arising in a highly re-entrant manufacturing system. By using a suitable Lyapunov function, we prove sufficient and necessary conditions on ISS. We also analyze the numerical discretization of ISS for a discrete scalar conservation law with nonlocal velocity and measurement error. A suitable discretized Lyapunov function is also analyzed to provide ISS of an equilibrium for the numerical approximation. Finally, we show numerical simulations to validate the theoretical findings.
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