Mean-square exponential stablization of memristive neuralnetworks: Deal

This paper investigates the mean-square exponential stabilization (MSES) of memristive neural
networks (MNNs) under replay attacks and communication interruptions. The research will
revolve around the following two questions: Firstly, facing replay attacks and communication
interruptions, how to design an appropriate controller? Secondly, how to ensure the MSES of
MNNs under higher replay attack rate and communication interruption rate? To address these
challenges, a novel intermittent sampled-data control scheme is established by considering the
mathematical characteristics of replay attacks and communication interruptions. Furthermore,
interval-dependent Lyapunov functions are constructed based on the Lyapunov stability theory
and inequalities techniques, and two sufficient criteria for MSES of MNNs under the mentioned
risks are derived. Thus, the control gain is obtained by solving a series of linear matrix
inequalities. In addition, two algorithms are designed to investigate the maximum allowable
replay attack rate and communication interruption rate for the system, respectively. Finally,
two numerical examples are given to verify the effectiveness of the proposed scheme.