Pinning synchronization of dynamical neural networks with hybrid delays via event-triggered impulsive control

In this study, a new event-triggered impulsive control strategy is used to solve the problem of pinning synchronization in coupled impulsive dynamical neural networks with hybrid delays. In view of discontinuous coupling terms and system dynamics, the inner delay and the impulsive delay are both investigated. Compared with the traditional pinning impulsive control, event-triggered pinning impulsive control (EPIC) generates impulse instants only when an event occurs, and is therefore more in line with practical applications. In order to deal with the complexities of mixed delays, some generalized inequalities related to hybrid delays based on Lyapunov functions are proposed, which are subject to the designed event-triggered rule. Then, in order to ensure network synchronization, linear matrix inequalities (LMIs) can provide some sufficient conditions with less conservatism while a proposed event-triggered function could successfully eliminate Zeno behavior. In addition, numerical examples are presented to prove the feasibility of the presented EPIC method.