Closeness-Centrality-Based Synchronization Criteria for Complex Dynamical Networks With Interval Time-Varying Coupling Delays
研究了具有区间时变时滞的复杂动态网络同步问题，将社会科学中的接近中心性引入网络模型，基于李雅普诺夫泛函和线性矩阵不等式给出同步稳定性的充分条件，并通过算例展示其在时滞鲁棒性上的优势。
This paper investigates synchronization in complex dynamical networks (CDNs) with interval time-varying delays. The CDNs are representative of systems composed of a large number of interconnected dynamical units, and for the purpose of the mathematical analysis, the leading work is to model them as graphs whose nodes represent the dynamical units. At this time, we take note of the importance of each node in networks. One way, in this paper, is that the closeness-centrality mentioned in the field of social science is grafted onto the CDNs. By constructing a suitable Lyapunov-Krasovskii functional, and utilizing some mathematical techniques, the sufficient and closeness-centrality-based conditions for synchronization stability of the networks are established in terms of linear matrix inequalities. Ultimately, the use of the closeness-centrality can be weighted with regard to not only the interconnection relation among the nodes, which was utilized in the existing works but also more information about nodes. Here, the centrality will be added as the concerned information. Moreover, to avoid the computational burden causing the nonconvex term including the square of the time-varying delay, how to deal with it is applied by estimating it to the convex term including time-varying delay. Finally, two illustrative examples are given to show the advantage of the closeness-centrality in point of the robustness on time-delay.