Global Practical Stabilization of the Double Integrator System In the Presence of Output Saturation and a Bounded Disturbance

Abstract

In this paper we consider the problem of global practical stabilization of the double integrator system in the presence of output saturation and a bounded disturbance additive to the output. Because of the disturbance in the output, not all system states can be driven into an arbitrarily small set, as in the usual practical stabilization problem, the output can only be driven into a bounded set whose size is dependent on the bound of the disturbance. It is shown that there exist linear feedback laws that globally practically stabilize the double integrator system in the presence of output saturation and the bounded output disturbance, and we propose linear low gain based dynamic output feedback laws to solve the global practical stabilization problem. Simulation results illustrate the effectiveness of the proposed control design.