In this paper, the advanced analysis of linear discrete time varying multiplicative noise system in terms of anisotropy-based theory is considered. Accurate formulae for anisotropic norm of such system with mutually independent multiplicative noises and additive input disturbances are given. There two types of anisotropy-based bounded real lemmas were derived, the first one in terms of backward-time difference Riccati equations, the another one in terms of inequalities.