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This paper studies delay-range-dependent stability problem for linear systems with interval timevarying delay.A novel type of Lyapunov-Krasovskii functional which contain some triple-integral terms is introduced,and a tighter bounding technique is employment.Based on Lyapunov functional approach and linear matrix inequality technology,some improved delay-range-dependent stability conditions are derived without using either free-weighting matrices or model transformation.Numerical examples are given to show the effectiveness and less conservativeness of the proposed methods.