The paper deals with the analysis and the design of a class of robust discrete-time Variable Structure controllers of integral type. We refer to the Discontinuous Integral Control (DIC) as the basic technique for reducing the chattering of the system. A modified discretized version of the DIC algorithm is introduced and discussed. To cope with the case of systems having slow time-varying parameters, a new adaptive control structure is proposed and analyzed. The asymptotic stability of the controlled system is proved in the case of constant external disturbances. Finally, some simulation results on the velocity control of a DC motor end the paper.