  Consider a linear stochastic system whose initial state is a random vector
with a specified Gaussian distribution. Such a distribution may represent a
collection of particles abiding by the specified system dynamics. In recent
publications, we have shown that, provided the system is controllable, it is
always possible to steer the state covariance to any specified terminal
Gaussian distribution using state feedback. The purpose of the present work is
to show that, in the case where only partial state observation is available, a
necessary and sufficient condition for being able to steer the system to a
specified terminal Gaussian distribution for the state vector is that the
terminal state covariance be greater (in the positive-definite sense) than the
error covariance of a corresponding Kalman filter.
