  We address the path-wise control of systems described by a set of nonlinear
stochastic differential equations. For this class of systems, we introduce a
notion of stochastic relative degree and a change of coordinates which
transforms the dynamics to a stochastic normal form. The normal form is
instrumental for the design of a state-feedback control which linearises and
makes the dynamics deterministic. We observe that this control is idealistic,
i.e. it is not practically implementable because it employs a feedback of the
Brownian motion (which is never available) to cancel the noise. Using the
idealistic control as a starting point, we introduce a hybrid control
architecture which achieves \emph{practical} path-wise control. This hybrid
controller uses measurements of the state to perform periodic compensations for
the noise contribution to the dynamics. We prove that the hybrid controller
retrieves the idealistic performances in the limit as the compensating period
approaches zero. We address the problem of asymptotic output tracking, solving
it in the idealistic and in the practical framework. We finally validate the
theory by means of a numerical example.
