In this paper we study the global null controllability with bounded controls of perturbed linear discrete-time systems in Rⁿ . More explicitly, a globally null-controllable autonomous discrete-time system is perturbed by ‘suitably small’ terms V(k) and B(k) to obtain a system of the form x(k + 1) = [A + V(k)]x(k) + [B + B(k)]u(k) and sufficient conditions are given to ensure the global null controllability of the resulting perturbed system.