Dynamic analysis of delayed neural networks: Event-triggered impulsive Halanay inequality approach

This paper proposes a generalized impulsive Halanay inequality from the impulsive control standpoints, where the impulse action is event-triggered. Namely, the control task is executed when an external event generated by the state-dependent event-triggered mechanism (ETM) is activated, rather than at a fixed time. It is shown that under the proposed event-triggered impulsive control (ETIC) strategy, the solution of the underlying inequality is guaranteed to converge to zero asymptotically. Moreover, the key point is the introduction of monitoring value to ensure a positive minimum inter-execution time, which exactly assists ETIC with reducing the pressure of information transmission. Then, the generalized impulsive Halanay inequality with appropriate ETIC scheme is utilized to the analysis of delayed neural networks (DNNs). In particular, some synchronization and asymptotic stability criteria of DNNs are derived, where the design of impulsive controller is based on ETIC strategy. At last, some numerical examples are provided to illustrate the validity of the obtained results.