In this paper the robust stabilization problem for linear discrete-time descriptor systems is investigated. This means that the transfer function matrix of the system at hand is allowed to be improper or even polynomial, as the uncertainty acts on normalized coprime factors. The main results comprising explicit analytical formulas for the maximum stability margin and for the robust stabilizing controller are given in a realization based-setting and involve solutions of two algebraic Riccati equations, thus recapturing the same elegant simplicity and numerical easiness of the standard (proper) case.