Linear discrete finite-dimensional dynamical systems with uncertain parameters are considered. Using the methods based on the Riccati equation, necessary and sufficient conditions for quadratic stabilizability of systems with uncertainty on the state matrix and for the system with uncertainty on both state and input matrices are formulated and proved. Moverover, an algorithm for the design of the state feedback gain matrix is proposed. It is based on an iterative procedure that consists of solving a discrete Riccati equation at each iteration. The results obtained in the paper are generalizations to the discrete-time uncertain dynamical systems of the results given for stabilizing uncertain continuous-time linear systems with norm-bounded time-varying uncertainty: [

*K. Zhou* and

*P. P. Khargonekar*, Robust stabilization of linear systems with norm bounded time varying uncertainty, Syst. Control Lett. 10, 17-20 (1988; M.R. 89e:93056)]. Finally, a simple numerical example is presented.