Exponential synchronization for second-order nonlinear systems in complex dynamical networks with time-varying inner coupling via distributed event-triggered transmission strategy

This paper focuses on the exponential synchronization problem of complex dynamical networks (CDNs) with time-varying inner coupling via distributed event-triggered transmission strategy. Information update is driven by properly defined event, which depends on the measurement error. Each node is described as a second-order nonlinear dynamic system and only exchanges information with its neighboring nodes over a directed network. Suppose that the network communication topology contains a directed spanning tree. A sufficient condition for achieving exponential synchronization of second-order nonlinear systems in CDNs with time-varying inner coupling is derived. Detailed theoretical analysis on exponential synchronization is performed by the virtues of algebraic graph theory, distributed event-triggered transmission strategy, matrix inequality and the special Lyapunov stability analysis method. Moreover, the Zeno behavior is excluded as well by the strictly positive sampling intervals based on the upper right-hand Dini derivative. It is noted that the amount of communication among network nodes and network congestion have been significantly reduced so as to avoid the waste of network resources. Finally, a simulation example is given to show the effectiveness of the proposed exponential synchronization criteria.