Exponential synchronization of time-varying delayed complex-valued neural networks under hybrid impulsive controllers

This paper focuses on exponential synchronization for master-slave time-varying delayed complex-valued neural networks (CVNNs) under hybrid impulsive controllers. Hybrid impulsive controllers is the extension of impulsive controllers, which can simultaneously permit synchronizing as well as desynchronizing impulses in one impulsive sequence, i.e., hybrid impulses. We separate CVNNs into their real and imaginary parts, which leads to two real-valued neural networks (RVNNs). Based on the concepts of average impulsive interval (AII) and average impulsive gain (AIG), we find that master-slave exponential synchronization for the real and imaginary parts of CVNNs can be realized via hybrid impulsive control under certain conditions. By employing the Lyapunov method, sufficient criteria are established to guarantee synchronization of the given master-slave CVNNs. Finally, the validity of the obtained results is demonstrated via a numerical example.