论文标题
边界反馈分析，用于针对不均匀线性双曲线系统平衡法的输入到状态稳定，并具有加性干扰
A boundary feedback analysis for input-to-state-stabilisation of non-uniform linear hyperbolic systems of balance laws with additive disturbances
论文作者
论文摘要
讨论了具有加性干扰的平衡定律的非均匀线性双曲线系统的边界反馈稳定问题。定义了连续和相应的离散Lyapunov函数。使用输入到国家稳定性（ISS）$ l^2- $ lyapunov功能，证明了线性平衡系统解决方案的衰减。在离散框架中，采用了一阶有限卷方案。在这种情况下，可以明确得出衰减率。主要目的是证明Lyapunov的稳定性，用于$ l^2 $ norm用于线性双曲线平衡法系统，并在分析和数值上都具有添加剂干扰。通过使用数值计算来证明理论结果。
A boundary feedback stabilisation problem of non-uniform linear hyperbolic systems of balance laws with additive disturbance is discussed. A continuous and a corresponding discrete Lyapunov function is defined. Using an input-to-state-stability (ISS) $ L^2- $Lyapunov function, the decay of solutions of linear systems of balance laws is proved. In the discrete framework, a first-order finite volume scheme is employed. In such cases, the decay rates can be explicitly derived. The main objective is to prove the Lyapunov stability for the $L^2$-norm for linear hyperbolic systems of balance laws with additive disturbance both analytically and numerically. Theoretical results are demonstrated by using numerical computations.
