A new result on exponential stability of a linear differential system of first order with variable delays

Abstract

In this paper, we investigate exponential stabilization problem for a class of linear systems with two continuous variable delays such that they belong to given intervals, but not necessary to be differentiable. By aid of a suitable Lyapunov-Krasovskii functional, Leibniz-Newton’s formula and linear matrix inequalities (LMIs), we derive some new sufficient conditions for the exponential stability of the zero solution of the considered system.