Global stabilization of the discrete-time double integrator using a saturated linear state feedback controller

Abstract

This paper further studies the discrete-time double integrator. Earlier it has been shown by us that there exists a class of locally stabilizing saturated linear state feedbacks which cause periodic behavior for certain initial conditions and hence the closed-loop system is then not globally asymptotically stable. In this paper, we show that all the remaining locally stabilizing saturated linear state feedbacks globally stabilize the discrete time double integrator.