Abstract: The strict passivity of a class of discrete-time singular systems is analyzed. A sufficient and necessary condition is given by means of strict linear matrix inequality (LMI) for the systems to be admissible and strictly passive. Based on the passive analysis and aiming at the discrete-time systems in which both state and output equations involve the control, the condition that is admissible and strictly passive for the closed-loop system is also analyzed via LMI under the control of state feedback, and the design method of the controller is given. A simulation example is presented to illustrate the effectiveness of the proposed method and show that the condition of strict LMI is simpler and easier to draw the same conclusion in comparison with the condition of non-strict LMI.