Synchronization of neural networks with and without disturbance input via control Lyapunov function

In this paper, we focus on the control Lyapunov function (CLF) for a class of neural networks, both with and without disturbance input. First, we design an exponential controller using the quadratic program-based CLF (QP-CLF) method to address the drive-response synchronization of a class of neural networks. Second, we propose a robust controller based on the robust QP-CLF approach to ensure the input-to-state stability (ISS) of the closed-loop system, even in the presence of external disturbances or system uncertainties. Finally, we present two numerical examples to demonstrate the effectiveness of the proposed QP-CLF and robust QP-CLF methods, highlighting their capability to maintain stability and synchronization in both ideal and disturbed conditions. These examples provide valuable insights into the practical applicability of the proposed control strategies.