The convergence relation between ordinary and delay-integro-differential equations

Abstract

In this paper, we investigate the problem of exponential convergence of solutions for a class of non-linear delay-integro-differential equations. Using the global uniform exponential convergence of solutions of the corresponding differential equation without delay, we show that the solutions of delay-integro-differential equations will remain globally uniformly exponentially convergent provided that the time lag is small enough. Finally, a numerical example is given to illustrate the applicability of our results.