In the paper, results of investigations are presented on the solution of stabilization problem with discrete controls for linear stationary systems. Necessary and sufficient conditions are proposed for the solvability of this problem given any fixed value of discretization step. Collections of values of discretization step are constructed for which there is no solution for discrete stabilization problem, and also other collections for which the solvability conditions differ from those of continuous stabilization problem. Comparative analysis of sets of continuous and discrete stabilizing controls is presented in the cases when gain coefficients in continuous and discrete controls coincide.