Dynamic behavior of the discrete‐time double integrator with saturated locally stabilizing linear state feedback laws

SUMMARY The main contribution of this paper is to completely characterize the dynamic behavior of the discrete‐time double integrator with a saturated locally stabilizing linear state feedback law. In continuous‐time setting, any linear state feedback control law that locally stabilizes the double integrator also globally stabilizes the system in the presence of actuator saturation. In discrete‐time setting, the equivalent of the double integrator does not have the same property. In this paper, we completely characterize the global behavior of saturated locally stabilizing linear state feedback laws for the discrete‐time double integrator.