This study deals with the stabilisation of discrete-time linear systems subject to static finite-level quantisation on the control inputs. Two kinds of quantisers are considered: uniform and logarithmic. The modelling of the finite-level quantisation is obtained by the application of deadzone and saturation maps to an infinite-level quantiser. From this model, conditions for the synthesis of state feedback control laws guaranteeing the convergence of the trajectories to an attractor around the origin provided that the initial state belongs to a certain admissible set are proposed. These conditions can thus be incorporated in linear matrix inequality-based optimisation schemes to compute the stabilising gain while minimising the size of the attractor.