Abstract The time-varying network topology can significantly affect the stability of multi-agent systems. This paper examines the stability of leader–follower multi-agent systems with general linear dynamics and switching network topologies, which have applications in the platooning of connected vehicles. The switching interaction topology is modeled as a class of directed graphs in order to describe the information exchange between multi-agent systems, where the eigenvalues of every associated matrix are required to be positive real. The Hurwitz criterion and the Riccati inequality are used to design a distributed control law and estimate the convergence speed of the closed-loop system. A sufficient condition is provided for the stability of multi-agent systems under switching topologies. A common Lyapunov function is formulated to prove closed-loop stability for the directed network with switching topologies. The result is applied to a typical cyber–physical system—that is, a connected vehicle platoon—which illustrates the effectiveness of the proposed method.

中文翻译：

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正实特征值切换拓扑下一般线性动态多智能体系统的稳定性

摘要 时变网络拓扑结构对多智能体系统的稳定性有显着影响。本文研究了具有一般线性动力学和交换网络拓扑结构的领导者-跟随者多智能体系统的稳定性，这些系统在联网车辆的编队中具有应用。交换交互拓扑被建模为一类有向图，以描述多智能体系统之间的信息交换，其中每个关联矩阵的特征值都需要为正实数。使用 Hurwitz 准则和 Riccati 不等式设计分布式控制律并估计闭环系统的收敛速度。为多智能体系统在切换拓扑下的稳定性提供了充分条件。制定了一个通用的 Lyapunov 函数来证明具有切换拓扑结构的有向网络的闭环稳定性。结果应用于典型的信息物理系统 - 即连接的车辆排 - 这说明了所提出方法的有效性。