We consider the problem of anisotropy-based analysis of the robust quality linear discrete time-varying systems with finite horizon under random external disturbance. Uncertainty in the probability distributions of disturbance vectors is found with the information-theoretic notion of anisotropy and additional conditions on the first two moments. The quality of operation of the object is defined by the value of the anisotropic norm of the input-output matrix corresponding to the system. We show that computing the anisotropic norm of a time-varying system in the state space with non-centered disturbance is related to solving a system of difference matrix equations and equations of a special form. We show a sample computation of the anisotropic norm for a time-varying system with finite horizon.