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The paper addresses robust stability and stabilization for continuous time-delay systems with norm-bounded uncertainty. The delay is assumed time-varying with both its value and variation rate being bounded. Based on a new Lyapunov-Krasovskii functional and the application of delay partitioning and the free-weighting matrix techniques, a set of sufficient LMI conditions is obtained to ensure asymptotical stability of the nominal system. Since there is no product term of Lyapunov matrix with any system matrix, the robust stabilization problem of computing a state feedback gain to cope with the norm-bounded uncertainty can be solved with reduced conservativeness. Numerical examples are given to show the effectiveness and the improvement of the derived results.