On global external stochastic stabilization of linear systems with input saturation

We consider the problem of global external stochastic stabilization for linear plants with saturating actuators, driven by a stochastic external disturbance, and having random Gaussian-distributed initial conditions. The aim of this stabilization is to control such plants by a possibly nonlinear static state feedback law that achieves global asymptotic stability in the absence of disturbances, while guaranteeing a bounded variance of the state vector for all time in the presence of disturbances and Gaussian distributed initial conditions. Results for continuous-time open-loop critically stable plants have been obtained before. The goal of this paper is to extend this result to critically unstable plants. We view our contribution in this paper as a first critical step in solving the LQG control problem for linear systems subject to saturated inputs which is a research problem with a long history in our field.