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The admissibility issue of discrete singular systems was mainly studied. Applying restricted equivalent transformations of the discrete singular system， a new necessary and sufficient condition was proposed to ensure discrete singular system admissible. By introducing an intermediate matrix to configure partial poles of system matrix such that the closed-loop system is regular， a state feedback controller was designed to make the closed-loop system admissible. Using similar methods， the controller design problem of uncertain discrete singular systems was discussed as well， a sufficient condition of robust stabilization for uncertain discrete singular systems was obtained. All the methods proposed in this article are strictly linear matrix inequalities(LMI). Two numerical examples verify the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]