  This paper is aimed at extending the H-infinity Bounded Real Lemma to
stochastic systems under random disturbances with imprecisely known probability
distributions. The statistical uncertainty is measured in entropy theoretic
terms using the mean anisotropy functional. The disturbance attenuation
capabilities of the system are quantified by the anisotropic norm which is a
stochastic counterpart of the H-infinity norm. A state-space sufficient
criterion for the anisotropic norm of a linear discrete time invariant system
to be bounded by a given threshold value is derived. The resulting Strict
Anisotropic Norm Bounded Real Lemma involves an inequality on the determinant
of a positive definite matrix and a linear matrix inequality. It is shown that
slight reformulation of these conditions allows the anisotropic norm of a
system to be efficiently computed via convex optimization.
