Finite-time synchronization for multi-weighted complex networks with time-varying delay couplings under hybrid delayed impulse effects via dynamic event-triggered control

This paper is concerned with the finite-time synchronization (FNS) for a class of multi-weighted complex networks (MCNs) with time-varying delay couplings under hybrid delayed impulse effects. Firstly, a new finite-time stability (FTS) criterion is established for nonlinear time-varying delayed systems under hybrid delayed impulse effects, and the settling-time (ST), which is relevant to impulse gain and initial value of system, is estimated accurately. Secondly, a dynamical event-triggered controller is designed by introducing a novel internal dynamical variable. Under the designed event-triggering mechanism (ETM), by applying Lyapunov functional method, inequality analysis technique and the proposed the FTS criterion, the synchronization conditions are addressed in the form of linear matrix inequalities (LMIs). In addition, the exclusion of Zeno phenomenon is verified. At last, two practical simulation examples are provided to substantiate the reliability of the proposed control scheme and the validity of the obtained theoretical results.