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This paper deals with the problem of the delay-dependent guaranteed cost H∞ control for an improvement interval system with time-varying delay. The time-varying delay is assumed to be in an interval and the derivative of the interval time-varying delay is not restricted, and where only the upper and lower bounds are known, this allows a fast time-varying function. Based on the Lyapunov-Ktasovskii functional, which fractionizes the average delay not the lower bound and deal with easily lower bound to be 0, and free weighting matrices approach without using the general model transformation, and bounding technique to handle the uncertain nonlinear matrices between the B and K. A delay-dependent bounded real lemma (BRL) and then a criterion for existence a state feedback controller is established. This guarantees the cost function upper bound and disturbance attenuation lever for all admissible uncertainties. A comparison Numerical example is given to illustrate the effectiveness of the proposed design method.