Asymptotic behavior of second-order linear multi-agent dynamic systems in directed network
有向网络下二阶线性多个体动力学系统的渐近性

This paper investigates the asymptotical behavior of second-order linear multi-agent dynamic systems in a direct communication network, and the configuration relation between those systems and the system structure. We use the notion of inertia in classical mechanism to describe the asymptotic behavior of second-order systems. When the parameters of position-control and the parameters of velocity-control of the system satisfy some conditions, the system approaches to the inertia-state. Meanwhile, the basic independent systems uniformly approach to the individual inertia-states which are determined by system initial-conditions and Laplacian left-eigenvectors associated with the zero eigenvalue; while the dependent systems reach some inertia-states in the convex-combination of individual inertia-states of independent systems.