论文标题
在矩阵加权的时间变化网络上达成共识
Consensus on Matrix-weighted Time-varying Networks
论文作者
论文摘要
本文探讨了随着时变的矩阵 - 不向导网络的共识问题。首先，我们介绍了矩阵加权的积分网络，用于分析此类网络。在对时间变化网络的开关模式的轻度假设下，可以根据相应积分网络的矩阵值laplacian的无空空间来提供平均共识的必要条件和/或足够的条件。特别是，对于定期的矩阵加权时间变化的网络，从代数的角度获得了必要的足够条件以达到平均共识。此外，我们表明，如果具有周期$ t> 0 $的积分网络在时间跨度$ [0，t）$中具有正跨性树，则可以达到节点状态的平均共识。提供了模拟结果以证明理论分析。
This paper examines the consensus problem on time-varying matrix-weighed undirected networks. First, we introduce the matrix-weighted integral network for the analysis of such networks. Under mild assumptions on the switching pattern of the time-varying network, necessary and/or sufficient conditions for which average consensus can be achieved are then provided in terms of the null space of matrix-valued Laplacian of the corresponding integral network. In particular, for periodic matrix-weighted time-varying networks, necessary and sufficient conditions for reaching average consensus is obtained from an algebraic perspective. Moreover, we show that if the integral network with period $T>0$ has a positive spanning tree over the time span $[0,T)$, average consensus for the node states is achieved. Simulation results are provided to demonstrate the theoretical analysis.
