This work focused on the synchronization of stochastic complex networks with time-varying delays and state-dependent countably infinite-state Markovian switching under event-triggered impulsive control. A drive–response framework was adopted, and the synchronization problem was reduced to the $ p $-th moment exponential stability of an associated error system. The response network was regulated by a state-dependent impulsive mechanism whose triggering instants were generated by the evolution of the synchronization error, thereby avoiding unnecessary control updates. To handle the countably infinite switching state space, Lyapunov methods were combined with uniform strong exponential ergodicity of the switching process and mode-uniform coefficient bounds. Within this framework, a general Lyapunov-type criterion was first established for the error dynamics, and a more explicit coefficient-based criterion was then derived to facilitate verification in applications. These results yield sufficient conditions for $ p $-th moment exponential synchronization of the drive and response networks. In addition, an explicit positive lower bound on the inter-event intervals was obtained, which excludes Zeno behavior and ensures implementability of the proposed control law. Numerical experiments on a coupled Chua circuit network with finite-state switching were presented as a special-case illustration of the theory. The simulations showed that the proposed event-triggered impulsive strategy effectively suppresses the synchronization error while remaining consistent with the theoretical lower-bound estimate for the triggering intervals.
Citation: Zezhen Feng, Sihan Zhao, Jiqiang Feng, Chen Xu. State-dependent event-triggered impulsive synchronization of stochastic delayed networks under countably infinite-state Markovian switching[J]. AIMS Mathematics, 2026, 11(8): 26614-26639. doi: 10.3934/math.20261068
This work focused on the synchronization of stochastic complex networks with time-varying delays and state-dependent countably infinite-state Markovian switching under event-triggered impulsive control. A drive–response framework was adopted, and the synchronization problem was reduced to the $ p $-th moment exponential stability of an associated error system. The response network was regulated by a state-dependent impulsive mechanism whose triggering instants were generated by the evolution of the synchronization error, thereby avoiding unnecessary control updates. To handle the countably infinite switching state space, Lyapunov methods were combined with uniform strong exponential ergodicity of the switching process and mode-uniform coefficient bounds. Within this framework, a general Lyapunov-type criterion was first established for the error dynamics, and a more explicit coefficient-based criterion was then derived to facilitate verification in applications. These results yield sufficient conditions for $ p $-th moment exponential synchronization of the drive and response networks. In addition, an explicit positive lower bound on the inter-event intervals was obtained, which excludes Zeno behavior and ensures implementability of the proposed control law. Numerical experiments on a coupled Chua circuit network with finite-state switching were presented as a special-case illustration of the theory. The simulations showed that the proposed event-triggered impulsive strategy effectively suppresses the synchronization error while remaining consistent with the theoretical lower-bound estimate for the triggering intervals.
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Zezhen Feng, Sihan Zhao, Jiqiang Feng, Chen Xu. State-dependent event-triggered impulsive synchronization of stochastic delayed networks under countably infinite-state Markovian switching[J]. AIMS Mathematics, 2026, 11(8): 26614-26639. doi: 10.3934/math.20261068
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