Predefined-time synchronization for competitive neural networks with different time scales and external disturbances

Abstract

This paper presents a study on the predefined-time (PdT) and practical PdT synchronization of competitive neural networks (CNN) in the presence of different time scales and external disturbances. Two types of external disturbances, which satisfy Lipschitz or bounded conditions, are investigated respectively. The new PdT and practical PdT stability theorems are derived in singularly perturbed systems, where the final residual set is given in detail. By employing the newly derived stability theorems, novel autonomous controllers are designed without relying on a continuous linear term and time scale parameters, while enabling PdT or practical PdT synchronization for drive-response CNNs. Additionally, upper bounds for the settling time are estimated, allowing for adjusting the predefined synchronization times regardless of the initial conditions. Finally, numerical simulations are conducted to demonstrate the effectiveness of the main results.