Exponential bipartite synchronisation of stochastic signed networks via intermittent pinning discrete-time state observations control

This paper studies the exponential bipartite synchronisation in mean square (EBS-MS) of stochastic signed networks (SSNs) via periodically intermittent pinning control. It is important to note that intermittent control is an extension of existing literature, which depends on discrete observations instead of continuous observations during the work period. Additionally, only a small percentage of the network nodes are controlled by intermittent control. Several sufficient conditions are established by the Lyapunov method and graph theory. Especially, when the duration tau between two consecutive observations tends to zero, our control will degenerate into common periodically intermittent pinning control. Meanwhile, a corollary about the EBS-MS of SSNs is presented. Besides, theoretical results are applied to a single-link robot arm system and an oscillator system. Finally, numerical simulations are presented to show the feasibility of the theoretical results.