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

Global stabilization of the discrete-time double integrator using a saturated linear state feedback controller,International Journal of Robust and Non

Global stabilization of the discrete-time double integrator using a saturated linear state feedback controller  
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This paper further studies the discrete-time dou- ble 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. I. INTRODUCTION Linear systems subject to actuator saturation are ubiqui- tous and have been the subject of extensive study, see for instance two special issues, (1), (2), and references therein. Internal stabilization for this class of systems has a long history. Let us briefly review the literature on linear systems subject to actuator saturation. (5), (9) established that, global stabilization of linear systems subject to actuator saturation can be achieved if and only if the linear system in the absence of actuator saturation is stabilizable, and has all its open- loop poles in the closed left-half plane for continuous-time linear systems and in the closed unit disc for discrete-time linear systems (equivalently, asymptotically null controllable with bounded control). In general, this requires nonlinear feedback control laws. However, for certain cases, global
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