Fixed/Prescribed-Time Synchronization of Hybrid Delayed Fuzzy Inertial Memristive Neural Networks

This paper investigates the fixed/prescribed-time synchronization problem for fuzzy inertial memristive neural networks (FIMNNs) with hybrid delays. Within a unified framework, a comparative study was conducted on the interval matrix method and the maximum absolute value method with respect to the state-dependent switching parameters induced by memristive characteristics. Correspondingly, two different controllers are designed, with theorem constraints expressed algebraically and as LMIs. Numerical experiments demonstrate that, under identical initial system parameters, the interval matrix method constructs a Lyapunov–Krasovskii functional (LKF) incorporating an integral term, enabling finer handling of time-delay effects. As a result, it provides a more accurate estimate of the upper bound of the settling time (ST) compared to the maximum absolute value method, thereby achieving faster and more efficient synchronization control. Ultimately, the proposed results are applied to image encryption, thereby demonstrating its theoretical significance and practical utility.