Exponential Stability Results on Random and Fixed Time Impulsive Differential Systems with Infinite Delay

Abstract

In this paper, we investigated the stability criteria like an exponential and weakly exponential stable for random impulsive infinite delay differential systems (RIIDDS). Furthermore, we proved some extended exponential and weakly exponential stability results for RIIDDS by using the Lyapunov function and Razumikhin technique. Unlike other studies, we show that the stability behavior of the random time impulses is faster than the fixed time impulses. Finally, two examples were studied for comparative results of fixed and random time impulses it shows by simulation.

Keywords

• random impulses
• delay differential system
• Razumikhin technique
• Lyapunov function
• exponential stability