Exponential Synchronization in Memristive Neural Networks with Distributed Delays: Theoretical and Practical Analysis of Two Control Strategies

This study delves into the complex problem of achieving exponential synchronization in memristive neural networks (MNNs) characterized by distributed latency. By utilizing the innovative concept of driving response systems, combined with rigorous linear matrix inequality (LMI) methods and basic Lyapunov stability theorem, we explored two different control strategies: time-delay feedback controller and event triggered controller (ETC). Both controllers have been carefully designed to facilitate exponential synchronization within the MNNs framework. Our method not only demonstrates the theoretical elegance of these control strategies, but also emphasizes their practical feasibility, and rigorously proves that Zeno phenomenon will not occur under ETC, proving the rationality of the ETC. Then, through detailed numerical simulations, we validated the correctness and effectiveness of our findings. The results indicate that both controllers are capable of achieving the required exponential synchronization, highlighting their potential in real-world applications.