Global stabilization of discrete-time linear systems with bounded inputs

In this paper we present a technique to stabilize discrete-time linear systems with bounded inputs. Based on optimal control techniques, we construct a continuous bounded state feedback which leads to global asymptotic stabilization for the case where the open-loop system has all its eigenvalues with modulus less than or equal to one. If the open-loop system has eigenvalues with modulus greater than one, a region of attraction of the origin is obtained. The resulting state feedback can be seen as a pointwise linear feedback with state-dependent gains, which are defined in terms of a non-linear algebraic equation.