In this paper, we consider the stabilization of a wave equation with an unknown anti-stable injection on the left boundary and the control input on the right boundary, where there are both collocated and non-collocated measurements. A static output feedback control law is designed to stabilize the wave equation. The value ranges of the feedback gains are given, such that all eigenvalues of the closed-loop system are shown to be inside the left-half complex plane by applying the Nyquist criterion for distributed parameter systems. Then the exponential stability of the closed-loop system is established. Numerical simulations are presented to verify the effectiveness of the proposed feedback control law.

在本文中，我们考虑了在左边界上具有未知反稳定注入和在右边界上的控制输入的波动方程的稳定性，其中有并置和非并置测量。设计了静态输出反馈控制律来稳定波动方程。给出了反馈增益的取值范围，通过应用分布式参数系统的奈奎斯特准则，闭环系统的所有特征值都显示在左半复平面内。然后建立闭环系统的指数稳定性。数值模拟被提出来验证所提出的反馈控制律的有效性。