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This brief provides new stability criteria for a class of uncertain singular systems with multiple-state delays. By introducing the state transformation, the study of the robust stability for original systems is changed into the study of robust stability for the equivalent systems. Based on Lyapunov-Krasovskii functionals combining with LMI techniques, the robust stability problem of equivalent systems is studied. New delay-dependent robust stability criteria are given in terms of quadratic forms of state and LMI, which ensure the robust stability of original systems at the same time.