This paper mainly studies the problem of robust finite-time consensus for leader-following multi-agent systems in detail-balanced graphs. It is evident that the knowledge of the leader’s input will provide significant assistance to a follower in tracking the leader. For this reason, an observer is constructed to estimate the input of the leader for each follower. Compared with many existing works of leader-following consensus, we do not assume that the input of the leader is bounded, but assume instead that its derivative is bounded. Based on input observer, two discontinuous protocols are proposed firstly that require only the sign information of the differences between a given agent’s state and that of its neighbors. Then, the finite-time consensus and the upper-bound of the settling time are obtained by using matrix theory, Lyapunov control approach, and the algebraic graph theory. Finally, the availability of the theoretical results is demonstrated through an example.

本文主要研究细节均衡图中领导者跟随多主体系统的鲁棒有限时间一致性问题。显然，对领导者输入的了解将为跟踪者跟踪者提供重要帮助。因此，构造了观察者以估计每个跟随者的领导者的输入。与许多现有的领导者遵循共识的作品相比，我们不假设领导者的输入是有界的，而是假设其派生词是有界的。基于输入观察者，首先提出了两种不连续的协议，它们仅需要给定代理状态与其邻居状态之间的差异的符号信息。然后，利用矩阵理论获得有限时间共识和建立时间的上限，Lyapunov控制方法和代数图论。最后，通过一个例子证明了理论结果的有效性。