Abstract: Highlights•The p<math><mi is="true">p</mi></math>th moment exponential stability (p<math><mi is="true">p</mi></math>-ES) of stochastic delayed systems is given.•Based on event-triggered delayed impulsive control (ETDIC), sufficient conditions are developed.•The proposed control strategy removes the limitations on the size of time delays.•The Lyapunov Razumikhin method is adopted to handle the time-varying delay.•The ETM serves as a solution for synchronization problems in complex neural networks.
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