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In this paper, we study the dynamics of a linear control system with givenstate feedback control law in the presence of fast periodic sampling attemporal frequency $1/\delta$ ($0 < \delta \ll 1$), together with small whitenoise perturbations of size $\varepsilon$ ($0<\varepsilon \ll 1$) in the statedynamics. For the ensuing continuous-time stochastic process indexed by twosmall parameters $\varepsilon,\delta$, we obtain effective ordinary andstochastic differential equations describing the mean behavior and the typicalfluctuations about the mean in the limit as $\varepsilon,\delta \searrow 0$.The effective fluctuation process is found to vary, depending on whether$\delta \searrow 0$ faster than/at the same rate as/slower than $\varepsilon\searrow 0$. The most interesting case is found to be the one where$\delta,\varepsilon$ are comparable in size; here, the limiting stochasticdifferential equation for the fluctuations has both a diffusive term due to thesmall noise and an effective drift term which captures the cumulative effect ofthe fast sampling. In this regime, our results yield a time-inhomogeneousMarkov process which provides a strong (pathwise) approximation of the originalnon-Markovian process, together with estimates on the ensuing error. A simpleexample involving an infinite time horizon linear quadratic regulation problemillustrates the results.

Approximation of linear controlled dynamical systems with small random noise and fast periodic sampling