Synchronisation of second-order stochastic complex dynamical networks via intermittent pinning discrete observations control and their applications

In this study, the exponential synchronisation of second-order stochastic complex dynamical networks (SOSCDNs) is considered. A novel control called periodically intermittent pinning discrete observations control is proposed, which is based on discrete-time state observations instead of continuous-time state observations during the control time. To the authors' knowledge, the above control strategy has rarely been investigated in previous researches. Compared with the existing literature, there are no restrictions on the network topology structure in this study. Furthermore, by employing the Lyapunov method, stochastic analysis techniques, and matrix theory, a synchronisation criterion and a corollary about the exponential synchronisation of the SOSCDNs are presented. In particular, when the duration between two consecutive observations tends to zero, periodically intermittent pinning discrete observations control degenerates into periodically intermittent pinning control, and relevant corollaries are also derived. Finally, they applied theoretical results to single-link robot arm systems and oscillator systems. Meanwhile, the numerical simulations are performed to demonstrate the effectiveness of their results.