The problem of finding frequency-domain conditions which guarantee asymptotic stability with probability 1 of linear systems with a time-varying feedback controller and having white noise parameter variations is considered. It is shown that the stochastic version of the second method of Liapunov can be employed for deriving sufficient conditions for stability of such systems. Stability criteria are derived after taking into account restrictions on the gain as well as on the rate of change of the gain of the controller.