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This paper deals with H infin delay-scheduled control of linear systems with time-varying delays. First, a new model transformation is given which allows to provide a unified approach to stability analysis and state-feedback control synthesis for time-delay systems represented in "linear fractional transformation (LFT)" form. A new type of controller is then synthesized, where the state-feedback is scheduled by the value of the delay (delay-scheduled controllers). The results are provided in terms of linear matrix inequalities (LMIs) which are known to be efficiently solvable.