  This paper studies a class of random nonlinear systems with time-varying
delay, in which the $r$-order moment ($r\geq1$) of the random disturbance is
finite. Firstly, some general conditions are proposed to guarantee the
existence and uniqueness of the global solution to random nonlinear time-delay
systems. Secondly, some definitions and criteria on noise-to-state stability in
the moment sense and in probability sense are given by Lyapunov method
respectively. Finally, two regulation controllers are constructed respectively
for two corresponding random nonlinear time-delay systems and the effectiveness
of two proposed recursive procedures are demonstrated by two simulation
examples.
