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The problem of delay-dependent robust H infin control for uncertain singular systems with multiple state delays has been studied. Firstly, using linear matrix inequality (LMI) approach, an improved delay-dependent criterion is given to ensure the singular system to be regular, impulse free and stable with H infin performance. Based on this criterion, the problem is solved via state feedback controller, which guarantees that the closed-loop system is not only regular, impulse free and stable, but also satisfying a prescribed H infin performance condition for all admissible uncertainties. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.