Instead of estimating the upper bound of the settling time in traditional finite-time control methods, this paper considers the prespecified-time synchronization of Lur'e networks, in which the settling time can be preset according to the requirement of tasks. Some smooth controllers are designed to achieve the goal of synchronization in a prespecified time and to maintain the synchronization after that. In addition, without the help of signum function or fractional power state feedback, the proposed control protocols are based on regular feedback and are smooth everywhere. Finally, two numerical examples with Chua's circuits are carried out to substantiate the effectiveness of the proposed designs.

中文翻译：

---

具有平滑控制器的 Lur'e 网络的预定时间分布式同步

本文没有在传统的有限时间控制方法中估计建立时间的上界，而是考虑了Lur'e网络的预定时间同步，其中建立时间可以根据任务的需要预先设定。一些平滑控制器的设计目的是在预定时间内达到同步的目的，并在此之后保持同步。此外，在没有符号函数或分数功率状态反馈的帮助下，所提出的控制协议是基于定期反馈的，并且在任何地方都是平滑的。最后，用 Chua 的电路进行了两个数值例子，以证实所提出设计的有效性。