Adaptive Control Design and Fractional Differential Inequality Approach to Complete Synchronization Analysis on Caputo Delayed Quaternion-valued Network Systems

This article discusses the complete synchronization problem for the Caputo derivative quaternion-valued delayed neural networks (QVDNNs). A novel Caputo fractional differential inequality is constructed, and an algebraic inequality result is derived by using the Laplace transform. Applying such algebraic inequality result and designing an adaptive controller with Riemann-Liouville integral operator, the two complete synchronization criteria on the Caputo fractional QVDNNs are established based on the different Lyapunov functionals. The obtained results are presented in algebraic inequality forms, which can greatly reduce the computation complexities in checking the complete synchronization performance. Particularly, the advantages of the obtained criteria are obvious in dealing with high-dimensional network systems. Moreover, the validity of the proposed results is demonstrated by the numerical simulations.