讨论一类波动方程的输出反馈稳定问题. 考虑的波动方程既有不稳定项又有反稳定项, 因此通常 的 Backstepping 变换难以直接应用. 文章给出一种基于系统的 Backstepping 变换设计方法, 巧妙地解决了上述问题. 该文给出了控制系统的输出反馈法则, 并且证明了闭环系统是有限时间稳定的. 数值模拟说明该方法是非常有效的.

In this paper, we consider the output feedback stability of a class of wave equation. Both the unstable term and the anti-stable term are subjected to the wave equation. Hence, it is very difficult to use the conventional Backstepping design for the considered problem. A system based Backstepping design is proposed to cope with the problem. An output feedback law is given to stabilize the wave equation and the finite-time stability is proved. The numerical simulation illustrates that the propose method is quite effective.