Sun Wen, Guan Junxia, Lu Jinhu, Zheng Zhigang, Yu Xinghuo, Chen Shihua
IEEE Trans Neural Netw Learn Syst. 2020 Mar;31(3):960-971. doi: 10.1109/TNNLS.2019.2911926. Epub 2019 May 16.
Many networked systems display some kind of dynamics behaving in a style with both continuous and impulsive communications. The cooperation behaviors of these networked systems with continuous connected or impulsive connected or both connected topologies of communications are important to understand. This paper is devoted to the synchronization of the networked system with continuous and impulsive hybrid communications, where each topology of communication mode is not connected in every moment. Two kind of structures, i.e., fixed structure and switching structures, are taken into consideration. A general concept of directed spanning tree (DST) is proposed to describe the connectivity of the networked system with hybrid communication modes. The suitable Lyapunov functions are constructed to analyze the synchronization stability. It is showed that for fixed topology having a jointly DST, the networked system with continuous and impulsive hybrid communication modes will achieve asymptotic synchronization if the feedback gain matrix and the average impulsive interval are properly selected. The results are then extended to the switching case where the graph has a frequently jointly DST. Some simple examples are then given to illustrate the derived synchronization criteria.
许多网络系统表现出某种动态特性，其行为方式兼具连续通信和脉冲通信。理解这些具有连续连接、脉冲连接或两者皆有连接的通信拓扑结构的网络系统的合作行为非常重要。本文致力于研究具有连续和脉冲混合通信的网络系统的同步问题，其中每种通信模式拓扑并非在任何时刻都是连通的。考虑了两种结构，即固定结构和切换结构。提出了有向生成树（DST）的一般概念来描述具有混合通信模式的网络系统的连通性。构造了合适的李雅普诺夫函数来分析同步稳定性。结果表明，对于具有联合DST的固定拓扑结构，若适当选择反馈增益矩阵和平均脉冲间隔，具有连续和脉冲混合通信模式的网络系统将实现渐近同步。然后将这些结果推广到图具有频繁联合DST的切换情况。接着给出了一些简单例子来说明推导得到的同步准则。
