On the Asymptotic Stability a System With Nonlinear Perturbations and Constant Delay

Abstract

In this paper, we consider a nonlinear perturbed system of neutral delay integro-differential equations (NDIDEs). We prove two new theorems, Theorems 1 and 2, such that these theorems include sufficient conditions and are related to asymptotical stability of zero solution of the perturbed system of NDIDEs. The technique of the proofs depends upon the definitions of two new and more suitable Lyapunov-Krasovskii functionals (LKFs). When we compared the results of this paper with those found in the literature, our results improve and extend some classical results, and contribute new contents to the topic of NDIDEs and to the profession.