Slide Mode Control Based Finite and Fixed‐Time Projective Synchronization for Delayed Clifford‐Valued Neural Networks

ABSTRACT This work addresses the problem of projective synchronization for Clifford‐valued neural networks with constant delays. To overcome the noncommutativity inherent in Clifford algebra, the drive and response systems are reformulated into equivalent real‐valued models. Based on a sliding mode control framework, suitable sliding surfaces and controllers are designed to ensure projective synchronization. Using Lyapunov stability analysis, sufficient conditions are established to guarantee both finite‐time and fixed‐time convergence of the projective synchronization error. Compared with existing methods, the proposed approach provides less conservative conditions and faster convergence. Additionally, we apply the proposed results to an example from the literature, illustrating the general applicability and improved performance of the method. Numerical simulations further support the theoretical findings.