This paper investigates uncertain SDOSs (singular delta operator systems), regarding robust H∞ control and robust H∞ performance analysis. To ensure robust admissibility, we introduce the definition of generalized quadratic admissibility. Through LMI (linear matrix inequality), with the support of a necessary and sufficient condition, an uncertain singular delta operator system is generalized quadratically admissible with a prescribed performance. Then, based on these conclusions, the design problem of a robust H∞ controller is considered for uncertain SDOSs. In terms of an LMI, the existence condition of a suitable robust H∞ controller is derived, and the corresponding design method is also presented through the solution to the LMI. Also, a numerical example is adopted to show the efficiency of the theoretical results in this paper through Matlab-LMI toolbox.