We solve the problem of stabilizing a general class of linear first-order hyperbolic systems using actuation at both boundaries of the spatial domain. We design a novel Fredholm transformation similarly to backstepping approaches to derive a boundary controller and a boundary observer enabling stabilization by output feedback. This yields an explicit full-state feedback law that achieves the theoretical lower bound for convergence to zero.

中文翻译：

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异向线性耦合双曲偏微分方程的两侧边界稳定


我们解决了使用空间域两个边界处的驱动来稳定一类线性一阶双曲系统的问题。我们设计了一种新颖的 Fredholm 变换，类似于反步方法，以导出边界控制器和边界观察器，从而通过输出反馈实现稳定。这产生了一个明确的全状态反馈定律，该定律实现了收敛到零的理论下限。