In this article, exponential bipartite synchronization in mth 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 in mth 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.

中文翻译：

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脉冲控制的带马尔可夫切换的随机有符号网络的指数双向同步

在本文中，m中的指数二分同步研究了随机符号网络的第一个矩。与以前的工作不同，随机干扰和马尔可夫切换都被认为是有符号网络。值得强调的是，有符号网络的拓扑结构取决于马尔可夫交换，并且并非所有交换子网都必须牢固连接。另外，设计了一种脉冲控制器，以使具有马尔可夫开关的随机有符号网络实现双向同步。然后，利用李雅普诺夫方法和有向有向图理论，获得了两个同步准则。这些标准与有符号网络的拓扑结构，脉冲增益和反向平均脉冲间隔密切相关。此外，我们的理论结果被用于研究指数双部分同步。在工程中单链接机器人手臂的第m时刻，并给出了同步标准。最后，一些数值模拟表明了理论结果的有效性和可行性。