Exponential bipartite synchronization of random signed networks with Markovian switching via impulsive control

Abstract

SummaryIn this article, exponential bipartite synchronization inmth moment of random signed networks is studied. Different from previous work, both random disturbances and Markovian switching are considered into signed networks. It is worth emphasizing that the topological structure of signed networks depends on Markovian switching, and not all switching subnetworks are required to be strongly connected. In addition, an impulsive controller is designed to make random signed networks with Markovian switching achieve bipartite synchronization. Then, by using Lyapunov method and signed digraph theory, two synchronization criteria are obtained. These criteria have a close relationship with the topological structure of signed networks, the impulsive gain and the reverse average impulsive interval. Furthermore, our theoretical results are applied to studying exponential bipartite synchronization inmth moment of single‐link robot arms in engineering, and a synchronization criterion is given. Finally, some numerical simulations are shown to illustrate the effectiveness and feasibility of theoretical results.