Necessary and Sufficient Conditions for 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 objective 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 as well as for a chain of integrators have been obtained before. The goal of this technical note is to extend this result to critically unstable plants. We view our contribution in this technical note as a 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.