Loop gain under random feedback

Abstract

We consider the feedback connection of a plant M with a random matrix gain /spl Delta/, and study the statistical properties of the loop gain L = M/spl Delta/, under the hypothesis that the random feedback A has a unitarily invariant distribution. This setup has interesting connections with two open problems related to the /spl gamma/-entropy of the plant, and to a probabilistic version of the multivariate Nyquist criterion.