In this paper, we consider the problems of robust stability and control for the class of uncertain discrete-time linear systems with Frobenius norm-bounded parameter uncertainties in all matrices of the system and output equations. Necessary and sufficient conditions for the above problems are proposed. A linear static state feedback control law is designed, which is in terms of a Riccati inequality. The results obtained here show that the robust control problem of the uncertain system is equivalent to the control problem for a corresponding uncertainty-free system.