Projective lag synchronization for quaternion neural networks with semi-Markov switching and mixed delays via non-fragile sliding mode control

This paper presents a comprehensive analysis of non-fragile projective lag synchronization (PLS) in semi-Markov jumping quaternion-valued neural networks (SMQVNNs) with complex delay structures, encompassing leakage delay, proportional delays, and distributed delays. To address system uncertainties, a non-fragile controller is incorporated, while the benefits of sliding mode control (SMC) are leveraged to enhance robustness. The integration of non-fragile control and SMC enables the system to effectively mitigate uncertainties and disturbances. The sliding surface is formulated using integral terms to ascertain the existence of sliding motion, and the direct Lyapunov technique is used to prove the SMC's effectiveness in driving the error system towards the target sliding surface. Furthermore, the error system's stochastic asymptotic stability is examined, and a stability condition is formulated. Numerical simulations, along with comparative results, confirm that the proposed method achieves faster and more robust synchronization than existing control schemes.