  In this article, we focus on the global stabilizability problem for a class
of second order uncertain stochastic control systems, where both the drift term
and the diffusion term are nonlinear functions of the state variables and the
control variables. We will show that the widely applied
proportional-derivative(PD) control in engineering practice has the ability to
globally stabilize such systems in the mean square sense, provided that the
upper bounds of the partial derivatives of the nonlinear functions satisfy a
certain algebraic inequality. It will also be proved that the stabilizing PD
parameters can only be selected from a two dimensional bounded convex set,
which is a significant difference from the existing literature on PD controlled
uncertain stochastic systems. Moreover, a particular polynomial on these bounds
is introduced, which can be used to determine under what conditions the system
is not stabilizable by the PD control, and thus demonstrating the fundamental
limitations of PD control.
