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This paper describes controller design scheme for time-varying delay system. Firstly, a robust ℋ∞ state feedback controller design (stabilizing controller) is proposed, which is given by LMI formulation. Secondary, a new controller design with frequency dependent ℋ∞ performance weights is proposed. The method enables shaping of the norm of sensitivity function in frequency domain with associated weighting functions. The controller has structure which includes state feedback of variables in weighting function, which corresponds to the augmentation of plant states. In the paper, a numerical example and simulation results are also shown, which evaluates the performance of the proposed method by comparing the conventional methods.