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The guaranteed-cost control program via memoryless state feedback controllers is studied for a class of linear time varying delay systems with norm-bounded time varying parametric uncertainty and a given quadratic cost function. The time varying delays considered are assumed bounded but no information to be available. Sufficient conditions for the existence of guaranteed-cost controllers are given in terms of linear matrix inequalities (LMIs). A convex optimisation problem with LMI constraints is formulated to design the optimal guaranteed-cost controller which minimises the guaranteed cost of the closed-loop uncertain system.