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The problem of robust H∞ control was discussed for a class of interval singular systems with state delay. The purpose is the design of a state feedback controller such that the resulting closed-loop system is robust stable while the closed-loop transfer function satisfies a prescribed H∞-norm bound constraint. This problem is solved via the notion of generalized quadratic stabilization with H∞-norm bound. Necessary and sufficient condition for generalized quadratic stabilization with H∞-norm bound is derived. A required state feedback controller is also constructed. Finally, an example is given to illustrate the effectiveness of the method.