Event-triggered synchronization for second-order nodes in complex dynamical network with time-varying coupling matrices

The synchronization of second-order systems in complex dynamical networks (CDNs) with time-varying coupling matrices is investigated in this paper. By using the matrix inequalities, event-triggered scheme and graph theory, one important sufficient condition is obtained to ensure that the above-mentioned CDNs can achieve the exponential synchronization under the cooperatively directed spanning tree topology. Meanwhile, the specific Lyapunov stability analysis method is given. In addition, continuous communication is avoided through introducing an event-triggered scheme, so that the energy consumption and communication load are decreased. The Zeno behavior is excluded by applying the right upper Dini derivative, which avoid infinite triggers. At last, the effectiveness of the reported exponential synchronization condition is verified through simulation examples.