  We present a stochastic predictive controller for discrete time linear time
invariant systems under incomplete state information. Our approach is based on
a suitable choice of control policies, stability constraints, and employment of
a Kalman filter to estimate the states of the system from incomplete and
corrupt observations. We demonstrate that this approach yields a
computationally tractable problem that should be solved online periodically,
and that the resulting closed loop system is mean-square bounded for any
positive bound on the control actions. Our results allow one to tackle the
largest class of linear time invariant systems known to be amenable to
stochastic stabilization under bounded control actions via output feedback
stochastic predictive control.
