Event-triggered delayed impulsive control for nonlinear systems with application to complex neural networks.

This paper studies the Lyapunov stability of nonlinear systems and the synchronization of complex neural networks in the framework of event-triggered delayed impulsive control (ETDIC), where the effect of time delays in impulses is fully considered. Based on the Lyapunov-based event-triggered mechanism (ETM), some sufficient conditions are presented to avoid Zeno behavior and achieve globally asymptotical stability of the addressed system. In the framework of event-triggered impulse control (ETIC), control input is only generated at state-dependent triggered instants and there is no any control input during two consecutive triggered impulse instants, which can greatly reduce resource consumption and control waste. The contributions of this paper can be summarized as follows: Firstly, compared with the classical ETIC, our results not only provide the well-designed ETM to determine the impulse time sequence, but also fully extract the information of time delays in impulses and integrate it into the dynamic analysis of the system. Secondly, it is shown that the time delays in impulses in our results exhibit positive effects, that is, it may contribute to stabilizing a system and achieve better performance. Thirdly, as an application of ETDIC strategies, we apply the proposed theoretical results to synchronization problem of complex neural networks. Some sufficient conditions to ensure the synchronization of complex neural networks are presented, where the information of time delays in impulses is fully fetched in these conditions. Finally, two numerical examples are provided to show the effectiveness and validity of the theoretical results.