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In this brief, the problem of synchronization stability analysis for complex dynamical networks with a time-varying coupling delay is studied. The delay considered in this brief is assumed to vary over an interval where the lower and upper bounds are known. By dividing the interval time-varying delay into a constant and a time-varying part and using a delay-partitioning approach, a new Lyapunov-Krasovskii functional is constructed. Based on this, a new delay-range-dependent criterion is obtained in terms of linear matrix inequalities. A numerical example is provided to show the effectiveness of the proposed results.