  In this paper, we investigate constrained control of continuous-time linear
stochastic systems. We show that for certain system parameter settings,
constrained control policies can never achieve stabilization. Specifically, we
explore a class of control policies that are constrained to have a bounded
average second moment for Ito-type stochastic differential equations with
additive and multiplicative noise. We prove that in certain settings of the
system parameters and the bounding constant of the control constraint,
divergence of the second moment of the system state is inevitable regardless of
the initial state value and regardless of how the control policy is designed.
