SIAM Journal on Control and Optimization, Volume 58, Issue 6, Page 3161-3184, January 2020.
In this paper, we consider the uniform stabilization problem for a coupled 1-d variable coefficient wave equation with anti-dampings in the interior domain and joint difference-type control. We use the integral-type feedback control to stabilize the system, in which the integral kernel functions are regarded as parameters. Our goal in the present paper is to select appropriate kernel functions such that the closed-loop system is exponentially stable. We first choose an exponentially stable system as a target system. Meanwhile, we introduce an appropriate auxiliary system. After that we construct two transformations. The first one is used to establish the equivalence between the original controlled time-delay system and the auxiliary system. This step mainly removes the effect of input memory. The second one is used to establish the equivalence between the auxiliary system and the stable target system. This step is to eliminate the negative effect of the anti-damping. Herein we mainly give an approach to selecting parameter functions in both transformations and hence get an exponentially stable-type feedback controller. Finally, some simulations are used to show the effectiveness of the proposed controller.

中文翻译：

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具有阻尼和联合时滞控制的一维耦合波动方程的一致镇定。

SIAM控制与优化杂志，第58卷，第6期，第3161-3184页，2020年1月。
在本文中，我们考虑了耦合一维变系数波动方程在内部域具有抗阻尼和联合差分类型控制的一致稳定问题。我们使用积分型反馈控制来稳定系统，其中将积分核函数视为参数。我们在本文中的目标是选择合适的内核函数，以使闭环系统呈指数稳定。我们首先选择一个指数稳定的系统作为目标系统。同时，我们介绍合适的辅助系统。之后，我们构造两个转换。第一个用于建立原始受控时滞系统与辅助系统之间的等效性。此步骤主要消除输入存储器的影响。第二个用于建立辅助系统与稳定目标系统之间的等价关系。此步骤是为了消除抗阻尼的负面影响。在这里，我们主要给出在两种变换中选择参数函数的方法，从而得到指数稳定型反馈控制器。最后，一些仿真被用来证明所提出的控制器的有效性。