Stability of Variable-Time Impulsive Systems with Delays via Generalized Razumikhin Technique and Application to Impulsive Neural Networks

Abstract

This paper investigates the stability of variable-time impulsive systems with time delays. A novel stability result is obtained via the generalized Razumikhin technique. By viewing fixed-time impulsive systems as degenerative variable-time impulsive systems, a new stability result for fixed-time impulsive systems is also proposed. In order to demonstrate the effectiveness of the generalized Razumikhin technique, we give some comparison results with the existing stability criteria which are derived from the classical Razumikhin technique. Stability of impulsive neural networks and synchronization of complex networks are employed to indicate the effectiveness and the practicality of the theoretical results.