Impulsive disturbance on stability analysis of delayed quaternion-valued neural networks

Abstract

In reality, abrupt uncertainty phenomenon may disturb or even break the system stability. Under these circumstances, it is worthy of studying the stability criteria of impulsive disturbed systems. In this article, an impulsive disturbed neural network model with delays is constructed in quaternion space, and the exponential stability conditions of the delayed system are derived by utilizing generalized norms. Firstly, a general impulsive disturbed quaternion-valued delayed neural network (IQVDNN) is given by combining impulsive differential system with quaternion-valued neural networks. Since quaternion multiplication is noncommutative, the IQVDNN system is decomposed into real-valued impulsive delayed neural networks. Then, the generalized ∞-norm and 1-norm are used to research its stability, respectively. By constructing special Lyapunov-type functional, several exponential stability sufficient criteria are obtained, which can guarantee that the stability can’t be destroyed by abrupt impulsive perturbations. Finally, two numerical examples and their simulation figures are given to show the effectiveness of the obtained conclusions.