Stability and Boundedness Properties of Third Order Differential Equation With Variable Delay

Abstract

In this paper, we employ Lyapunov-Krasovskii approach to study sufficient conditions for uniform asymptotic stability, uniform boundedness and uniform ultimate boundedness of solutions to a certain system of third order delay differential equation when the vector H (X(t - r (t))) appearing in the equation is not necessarily differentiable. Two numerical examples are provided to authenticate the correctness of our results. Our results include, improve and generalize some established results in literature.