On the lower bound of the anisotropic norm of the linear stochastic system

Abstract

The anisotropic norm of the linear discrete time invariant system is the measure of the system output sensitivity to a random input with the mean anisotropy bounded by some nonnegative value a. The mean anisotropy characterizes the degree of predictability of the stochastic signal. The anisotropic norm of a system is the induced norm with the extreme cases of H₂ norm and H_∞ norm, respectively, under a → 0 and a → ∞. The lower bound of the anisotropic norm of the linear discrete time invariant system was established in the present paper using the methods of linear algebra.