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The problem of delay-dependent asymptotic stability for linear system with interval time-varying delay is investigated. Based on delay decomposition method, a new type of Lyapunov functional is constructed, which make use of the information on the lower bound of the delay and some delayed state sufficiently. Several less conservative delay-dependent stability criteria are presented by using the piecewise analysis method and a new convex combination technique. Numerical examples are given to demonstrate the effectiveness and less conservatism of the proposed method.