We consider a finite horizon linear discrete time varying system whose input is a random noise
with an imprecisely known probability law. The statistical uncertainty is described by a nonnegative
parameter a which constrains the anisotropy of the noise as an entropy theoretic measure of deviation
of the actual noise distribution from Gaussian white noise laws with scalar covariance matrices. The
worst-case disturbance attenuation capabilities of the system with respect to the statistically uncertain
random inputs are quantified by the a-anisotropic norm which is a constrained operator norm of the
system. We establish an anisotropic norm bounded real lemma which provides a state-space criterion
for the a-anisotropic norm of the system not to exceed a given threshold. The criterion is organized as
an inequality on the determinants of matrices associated with a difference Riccati equation and extends
the Bounded Real Lemma of the H¥-control theory. We also provide a necessary background on the
anisotropy-based robust performance analysis