Stabilisation of discrete‐time systems with finite‐level uniform and logarithmic quantisers

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