A discrete-time multiagent system with a fixed set of elements (particles) is studied. Particles synchronize with each other in accordance with a family of communication graphs. At each time instant (step), the system is described by a vector that updates iteratively: the state of each agent is linearly determined by the states of its neighbors and also by an additive random noise component; in addition, links between particles change over time. Thus, the system’s evolution can be modeled by an iterative process in which the state vector is multiplied by a certain stochastic matrix and added to a random vector. The goal of this paper is to analyze an index measuring the system’s closeness to a consensus. Some constraints on the family of communication graphs that are sufficient for obtaining an upper bound on this index are established. Also, a modified model in which the upper bound is satisfied under slightly weakened conditions on communication graphs is presented.

研究了具有固定元素集（粒子）的离散时间多主体系统。粒子根据一系列通信图彼此同步。在每个时刻（步骤），系统都由一个向量进行描述，该向量进行迭代更新：每个代理的状态由其邻居的状态以及附加的随机噪声分量线性确定；此外，粒子之间的联系会随着时间而变化。因此，可以通过迭代过程对系统的演化进行建模，在迭代过程中，状态向量乘以某个随机矩阵，然后添加到随机向量中。本文的目的是分析衡量该系统与共识的接近程度的指标。在通信图族上建立了一些足以获得该索引上限的约束。也，