Uniform asymptotic stability for the perturbations of linear delay systems

Abstract

This work provides necessary and sufficient conditions for the exponential asymptotic stability in the large and uniform asymptotic stability of perturbations of linear delay systems. A strong relationship is established between the two types of asymptotic stability. It is found that if the exponential estimate of the solution of a system tends to zero as time, t, tends to infinity, the system is said to be uniformly asymptotically stable. Stability criteria for the linear part of the system is derived and with enough smoothness conditions on the perturbation function and an appeal made to Lyapunov’s stability results and some Gronwall’s type inequailities, the required stability results are established for linear perturbations.