This article explores the novel approach to addressing the intra/inter-layer synchronization challenges in stochastic multi-layer networks (SMLNs). First, considering the influence of time delay in control, an event-triggered delayed impulsive control (ETDIC) strategy is developed, where the impulsive instant is determined by the predesigned event-triggered mechanism. Moreover, by introducing piecewise auxiliary functions, it effectively excludes Zeno behavior within the ETDIC framework. The study then derives sufficient conditions for ensuring intra- and inter-layer; synchronization, leveraging the Lyapunov method and rigorous mathematical analysis. Finally, theoretical results are validated through numerical simulations.
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