Sliding mode synchronization control of delayed quaternion-valued neural networks and its application

This paper uses a non-decomposition method to study the sliding mode synchronization problem of a quaternion-valued neural network model with delay and external disturbance. The process involves designing a disturbance observer for the error system and selecting a suitable integral sliding surface. Based on this, an effective sliding mode controller is designed. The paper then presents the sufficient criterion for sliding mode synchronization, obtained using the inequality technique by constructing a Lyapunov function independent of the time delay. The reachability analysis of the sliding surface is also provided, enabling the state trajectory of the closed-loop dynamic error system to be driven to the predetermined sliding surface within a limited time. The paper concludes with the verification of the research’s conclusions through numerical examples. The research is applied to image encryption and decryption, demonstrating the practical relevance of the findings, and valid statistical comparisons are also conducted.