Robust Stabilization of Linear Systems in the Presence of Unbounded Uncertain Parameters with Applications to Yaw Stabilization of a Satellite

We consider the problem of stabilization of linear systems in the presence of uncertain parameters which are described by Gaussian white noise processes. We present a methodology for finding a state feedback controller that make the closed loop system exponentially stable in the mean square sense as well as almost sure sense. This leads to a direct method of synthesizing feedback controllers for stabilizing the system at a prespecified rate. This result is analogous to the well-known pole placement result of linear deterministic systems. A consequence of this result is a controller-failure-proof system which will not be destabilized in the events of controller failure. The results are applied to the yaw stabilization of a satellite by geomagnetic fields.