Image Encryption via Sliding Mode Synchronization of Fractional-Order Quaternion-Valued T–S Fuzzy Neural Networks With Uncertain Parameters

This paper explores the sliding mode synchronization issue in a fractional-order quaternion-valued Takagi-Sugeno fuzzy neural network model with parametric uncertainty using a non-decompositional approach. An integral sliding surface is developed, and a sliding mode controller is designed based on the principles of sliding mode control. To ensure synchronization, we construct a Lyapunov function and apply fractional-order theory, quaternion theory, and inequality analysis to establish a criterion that is sufficient to ensure that the systems achieve synchronization via sliding mode control. Furthermore, we perform a reachability analysis on the sliding surface. Finally, we verify our conclusions through numerical examples and apply our research findings to image encryption and decryption. Simulation results demonstrate that the research method presented in this paper effectively enhances security and improves encryption efficiency in color image encryption, while maintaining high image restoration quality.