Exponential bipartite synchronization of delayed coupled systems over signed graphs with Markovian switching via intermittent control. Issue 3 (February 2021)

• Record Type: Journal Article
• Authors: Wang, Mengxin; Guo, Jia; Qin, Sitian; Feng, Jiqiang; Li, Wenxue
• Is Part Of: Journal of the Franklin Institute. Volume 358:Issue 3(2021)
• Page Start: 2060
• Page End: 2085
• Publication Date: 2021-02
• Subjects: Science -- Periodicals; Technology -- Periodicals; Patents -- United States -- Periodicals; 505
• DOI: 10.1016/j.jfranklin.2020.12.031
• Languages: English
• ISSNs: 0016-0032

Abstract

Abstract: Throughout this paper, we focus on the exponential bipartite synchronization of delayed coupled systems over signed graphs via intermittent control. It is worth noting that the intermittent control utilized is aperiodic. And this is the first time that discontinuous control is applied to studying the bipartite synchronization of systems over signed graphs. Meanwhile, the topological structure of delayed coupled systems over signed graphs depends on Markovian switching, and not all switching subgraphs are required to be strongly connected. By virtue of Kirchhoff's Matrix Tree Theorem in graph theory, Lyapunov method and differential inequality techniques, some synchronization criteria are obtained to ensure the exponential bipartite synchronization in p th moment of systems over signed graphs. Theoretical results developed herein are illustrated by practical examples about coupled single-link robot arms and coupled oscillators, respectively and a sufficient criterion is given. Meanwhile, the corresponding numerical simulations are given to demonstrate the validity and feasibility of theoretical results.