This paper deals with the class of linear discrete-time systems with varying time-delay. The problems of stability and stabilizability for this class of systems are considered. Given an upper and a lower bounds on the time-varying delay sufficient conditions for checking the stability of this class of systems are developed. A control design algorithm is also provided. All the results developed in this paper are in the LMI formalism which makes their solvability easier using existing tools. A numerical example is provided to show the effectiveness of the established results.