On external semi-global stochastic stabilization of a double integrator with input saturation

This paper considers external semi-global stochastic stabilization for linear plants with saturating actuators, driven by a stochastic external disturbance, and having random Gaussian-distributed initial conditions. Recently, it has been shown that for critically stable systems there exists a linear static state feedback law that achieves global asymptotic stability in the absence of disturbances, while guaranteeing a bounded variance of the state vector in the presence of disturbances and Gaussian distributed initial conditions. We report how this result extends to a double integrator with input saturation.