We solve in this article the problem of robust output feedback regulation for a system composed of two hyperbolic equations with collocated input and output in presence of a general class of disturbances and noise. Importantly, the robustness of the controller is considered with respect to delays in the actuation and in the measurements but also with respect to uncertainties on parameters, most importantly transport velocities. The proposed control law introduces three degrees of freedom (by means of tuning parameters) on which we give general conditions to guarantee the existence of robustness margins. We show that to tune these degrees of freedom and allow potential robustness trade-offs, it is necessary to consider all the different types of uncertainties simultaneously as it is the only way to ensure the existence of non-zero robustness margins. Provided that these conditions are satisfied, these tuning parameters enable a trade-off between performance and robustness, between disturbance rejection and sensitivity to noise. The existence of robustness margins and the Input To State Stability of the system are proved combining backstepping transformations and classical complex analysis techniques.

在本文中，我们解决了由两个双曲型方程组成的系统的鲁棒输出反馈调节的问题，该系统在存在一般干扰和噪声的情况下将输入和输出并置。重要的是，控制器的鲁棒性不仅要考虑驱动和测量中的延迟，还要考虑参数的不确定性，最重要的是运输速度。拟议的控制定律引入了三个自由度（通过调整参数），在这些自由度上我们给出了保证存在鲁棒裕度的一般条件。我们证明了要调整这些自由度并允许潜在的鲁棒性折衷，必须同时考虑所有不同类型的不确定性，因为这是确保存在非零鲁棒性余量的唯一方法。只要满足这些条件，这些调整参数就可以在性能与鲁棒性，干扰抑制与噪声敏感性之间进行权衡。结合反推变换和经典复杂分析技术，证明了系统的鲁棒裕度和输入状态稳定性的存在。