Robust exponential stability of fractional-order coupled quaternion-valued neural networks with parametric uncertainties and impulsive effects

Abstract This paper investigates the robust exponential stability (RES) issue for fractional-order coupled quaternion-valued neural networks (FCQNNs) with parametric uncertainties and impulsive effects. According to the rules of quaternion algebra and its properties, a new fractional-order inequality is built, which greatly generalizes the existing fractional-order inequality in the real domain. On the basis of quaternion inequality technique, newly established inequality, together with algebraic graph theory and iterative method, several criteria for easy verification are presented, which depend on not only impulsive gain and maximum impulsive interval but also the scale of the controlled vertices. Furthermore, the convergence rate of the considered FCQNN is also estimated. Finally, numerical results are given to substantiate our theoretical criteria.