An asymptotic formula is obtained for the optimal anisotropic controller for linear discrete time-invariant system driven by random disturbance with infinitesimal mean anisotropy. The result is accompanied with the asymptotic formula for the anisotropic norm of the closedloop system. An upper bound is computed for the mean anisotropy at which the optimal anisotropic controller can be approximated by the H2-optimal controller with loss in performance gain less than a given threshold.