Global finite-time stability of delayed quaternion-valued neural networks based on a class of extended Lyapunov–Razumikhin methods

In this paper, a class of global finite-time stability problem for quaternion-valued neural networks with time-varying delays are investigated by adopting an extended modification Lyapunov–Razumikhin (L–R) method and a new upper bounds estimation of system solution in terms of convergence rate was obtained. Firstly, a new extended method of L–R is proposed to solve the general difficulty to find a proper Lyapunov functional. Then, a new suitable controller is designed, the new conditions of inequalities global finite-time stability are obtained via combining with the former proposed L–R method in the separated real-valued system. Finally, for purpose of verifying the availability of the theorem presented, two given illustrative examples are shown.