  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 an appropriately 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-infinity-control theory. We also
provide a necessary background on the anisotropy-based robust performance
analysis.
