This paper presents some results on absolute stabilization of nonlinear discrete-time systems under control saturations. The studied control law consists of the feedback of both the states and of the nonlinearity present in the dynamics of the controlled system. Saturations are taken into account by modelling the nonlinear saturated system through deadzone nonlinearities satisfying a modified sector condition. Thus, as for continuous-time systems, LMI absolute stabilization conditions are proposed for the design of the feedback gains, both in the local and global stability contexts. Some relations of the proposed results with the dissipativity and passivity theory are included and a numerical example is reported