In this paper, an asymptotic representation is obtained for the optimal anisotropic dynamical output feedback controller for linear discrete time-invariant systems and for the anisotropic norm of the closed-loop system with such a controller. Also, the maximum value of the mean anisotropy of the external disturbance, at which the optimal anisotropic controller is approximated by the H2-optimal controller with a given accuracy, is established. The numerical example of optimal anisotropic control problem solution for the linear discrete time-invariant system is illustrated by the graphs.