We study the anti-disturbance problem of a 1-d wave equation with boundary control matched disturbance. In earlier literature, the authors always designed the controller such as the sliding mode control and the active disturbance rejection control to stabilize the system. However, most of the corresponding closed-loop systems are boundedly stable. In this paper we show that the linear feedback control also has a property of anti-disturbance, even if the disturbance includes some information of the system. By choosing suitable parameters introduced in the proof, we can ensure the solution of the closed-loop system is bounded in an admissible range. As an application, we discuss the control problem of a nonlinear system. As a result, it is shown that the bounded estimation of the solution is suitable.

中文翻译：

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具有边界控制匹配扰动的一维波动方程闭环系统的抗扰性

我们研究了具有边界控制匹配扰动的一维波动方程的抗扰动问题。在早期的文献中，作者总是设计滑模控制和自抗扰控制等控制器来稳定系统。然而，大多数相应的闭环系统都是有界稳定的。在本文中，我们表明线性反馈控制也具有抗干扰特性，即使干扰包括系统的某些信息。通过选择证明中引入的合适参数，我们可以确保闭环系统的解在一个可接受的范围内。作为一个应用，我们讨论非线性系统的控制问题。结果表明，解的有界估计是合适的。