This paper proposes a new distributed finite-time differentiator (DFD) for multi-agent systems (MAS) under directed graph, which extends the differentiator algorithm from the centralized case to the distributed case by only using relative/absolute position information. By skillfully constructing a Lyapunov function, the finite-time stability of the closed-loop system under DFD is proved. Inspired by the duality principle of control theory, a distributed continuous finite-time output consensus algorithm extended from DFD for a class of leader-follower MAS is provided, which not only completely suppresses disturbance, but also avoids chattering. Finally, several simulation examples are given to verify the effectiveness of the DFD.

翻译：本文针对有向图下的多智能体系统提出一种新型分布式有限时间微分器，通过仅利用相对/绝对位置信息，将集中式微分器算法拓展至分布式场景。通过巧妙构造李雅普诺夫函数，证明了闭环系统在分布式有限时间微分器作用下的有限时间稳定性。受控制理论对偶原理启发，进一步提出基于该分布式有限时间微分器的一类领导者-跟随者多智能体系统分布式连续有限时间输出一致性算法，该算法不仅能完全抑制扰动，还可避免抖振现象。最后，通过若干仿真算例验证了所提出分布式有限时间微分器的有效性。