We consider the problem of boundary feedback control of single-input-single-output one-dimensional linear hyperbolic systems when sensing and actuation are anti-located. The main issue of the output feedback stabilization is that it requires dynamic control laws that include delayed values of the output (directly or through state observers) which may not be robust to infinitesimal uncertainties on the characteristic velocities. The purpose of this paper is to highlight some features of this problem by addressing the feedback stabilization of an unstable open-loop system which is made up of two interconnected transport equations and provided with anti-located boundary sensing and actuation. The main contribution is to show that the robustness of the control against delay uncertainties is recovered as soon as an arbitrary small diffusion is present in the system. Our analysis also reveals that the effect of diffusion on stability is far from being an obvious issue by exhibiting an alternative simple example where the presence of diffusion has a destabilizing effect instead.

我们考虑传感和驱动反定位时单输入单输出一维线性双曲线系统的边界反馈控制问题。输出反馈稳定的主要问题是它需要动态控制法则，其中包括输出的延迟值（直接或通过状态观察器），这可能对特征速度的无穷小不确定性不稳健。本文的目的是通过解决不稳定开环系统的反馈稳定问题来突出这个问题的一些特征，该系统由两个相互关联的传输方程组成，并提供反定位边界传感和驱动。主要贡献是表明一旦系统中存在任意小扩散，控制对延迟不确定性的稳健性就会恢复。我们的分析还表明，扩散对稳定性的影响远非一个明显的问题，方法是展示一个替代的简单示例，其中扩散的存在反而会产生不稳定的影响。