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This paper is focused on the absolute stability of Lur’e systems with time-varying delay. Based on the quadratic separation framework, a complete delay-decomposing Lyapunov-Krasovskii functional is constructed. By considering the relationship between the time-varying delay and its varying interval, improved delay-dependent absolute stability conditions in terms of linear matrix inequalities (LMIs) are obtained. Moreover, the derived conditions are extended to systems with time-varying structured uncertainties. Finally, a numerical example is given to show the advantage over existing literatures.