In this paper, we respectively discuss the finite-time consensus (FTC) and finite-time $H_{\infty }$ consensus (FTHC) problems for a kind of nonlinear multi-agent systems under directed topology. Firstly, with the help of some inequality techniques and the designed state feedback controller, a FTC criterion is presented for multi-agent system. In addition, two adaptive control strategies for ensuring the FTC of multi-agent system are also developed. Moreover, we further discuss the FTHC for multi-agent system with external disturbances, and some FTHC criteria are given by exploiting the designed state feedback controller and adaptive state feedback controllers. Finally, the effectiveness of these obtained results are verified by two numerical examples.

中文翻译：

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定向拓扑下多代理系统的有限时间共识和有限时间$H_{\infty}$共识

在本文中，我们分别讨论了一种有向拓扑下非线性多智能体系统的有限时间共识（FTC）和有限时间$H_{\infty}$共识（FTHC）问题。首先，借助一些不等式技术和设计的状态反馈控制器，提出了多智能体系统的FTC准则。此外，还开发了两种用于确保多智能体系统 FTC 的自适应控制策略。此外，我们进一步讨论了具有外部干扰的多智能体系统的 FTHC，并通过利用设计的状态反馈控制器和自适应状态反馈控制器给出了一些 FTHC 准则。最后，通过两个数值算例验证了所得结果的有效性。