In this paper, we consider boundary stabilization for a one-dimensional wave equation subject to periodic disturbance. By regarding the periodic signal as a boundary output of a free wave equation, we transform the controlled plant into a coupled wave system. We first design a state observer for the coupled system to estimate the disturbance and the system state simultaneously. An output feedback control is then designed to stabilize the original system. As an application, the result is applied to the stabilization of a wave equation with periodic disturbance suffering in output. Finally, some simulations are presented to validate the theoretical results.

中文翻译：

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周期扰动波动方程的渐近稳定

在本文中，我们考虑一维波动方程在周期扰动下的边界稳定。通过将周期信号视为自由波方程的边界输出，我们将受控设备转换为耦合波系统。我们首先为耦合系统设计一个状态观测器，以同时估计干扰和系统状态。然后设计输出反馈控制来稳定原始系统。作为一种应用，该结果可应用于在输出中遭受周期性干扰的波动方程的稳定化。最后，提出了一些仿真来验证理论结果。