Using Lyapunov first method instead of traditional Lyapunov second method, this paper focuses on studying the consensus tracking control problem of multi-agent systems (MASs) with time-varying delays and arbitrary adjacent weights under fixed topology and switching topology, respectively. We first give four equivalent criteria for MASs with fixed communication topology, where the positive stability of matrix H : = L + B (L is the Laplacian matrix of G , B is the leader’s adjacency matrix) not only plays a key role as usual but also becomes an urgent and more complicated problem due to the introduction of negative weights in MASs. Second, for MASs with switching communication topology if the average dwell time of switching topology, the total activation time of stable subsystems and the upper bound of time delay satisfy some conditions, then MASs with all stable subsystems (partially stable subsystems) can achieve consensus tracking. Finally, simulations are given to demonstrate the effectiveness of our theoretical results.

中文翻译：

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具有时变延迟和任意权重的二阶多智能体系统的领导者跟随共识

使用李雅普诺夫第一方法代替传统的李雅普诺夫第二方法，本文重点研究固定拓扑和交换拓扑下时滞和任意相邻权重的多智能体系统（MAS）的一致性跟踪控制问题。我们首先给出了具有固定通信拓扑结构的 MAS 的四个等效标准，其中矩阵 H 的正稳定性：= L + B（L 是 G 的拉普拉斯矩阵，B 是领导者的邻接矩阵）不仅像往常一样起关键作用，而且由于在 MAS 中引入了负权重，这也成为一个紧迫且更复杂的问题。其次，对于具有切换通信拓扑结构的 MAS，如果切换拓扑结构的平均停留时间、稳定子系统的总激活时间和时延上限满足一些条件，那么具有所有稳定子系统（部分稳定子系统）的 MAS 可以实现共识跟踪。最后，给出了模拟以证明我们的理论结果的有效性。