μ-stability of infinite delay functional differential systems with impulsive effects

Abstract

In this article, a new concept of μ-stability for impulsive functional differential systems is proposed, which unifies uniform stability, uniform asymptotic stability, exponential stability, etc. Using the improved Razumikhin technique and Lyapunov functions, we obtain some sufficient conditions to ensure the μ-stability of functional differential systems with infinite delays under impulsive perturbations. The results obtained in this article improve and extend existing results and provide another set of criteria for determining the stability of impulsive infinite delay different systems. An example is given to illustrate the effectiveness and advantages of the results.

Keywords:

• impulsive functional differential systems
• infinite delays
• μ-stability
• improved Razumikhin technique
• Lyapunov functions

AMS Subject Classifications:

• 34A37
• 34D23