Global exponential stability of nonlinear time-delay system under impulsive control with distributed delay

This paper investigates the global exponential stability of nonlinear time-delay system (NTDS) under impulsive control with distributed delay. By establishing a connection between the distributed delay in impulsive control and the number of impulsive times, a novel Razumikhin-type impulsive inequality is formulated. Using this inequality and the concept of the average impulsive interval, some delay-independent sufficient conditions of the global exponential stability of NTDS are derived. This indicates that the upper bounds of the impulsive interval and state time delay are no longer constrained, and the mutual constraint between the distributed delay in impulse and state time delay is removed, which greatly improves the results of recent studies. Finally, two numerical examples are presented to showcase the validity and practicality of the results.