Stability of quaternion-valued impulsive delay difference systems and its application to neural networks

In this paper, we make first attempt to investigate exponential stability for quaternion-valued impulsive delay difference systems. By employing Lyapunov methods and quaternion-modulus inequality technique, sufficient conditions for the exponential stability are presented. In addition, as a subsequent result, the obtained theory is successfully applied to study a class of discrete-time quaternion-valued impulsive neural networks with delay. Finally, a numerical example is given to illustrate the effectiveness of theoretical results.