ON STABLE SYSTEMS WITH RANDOM STRUCTURE\ast

We study the stability of linear systems with a random structure, where a system structure is described as a vector space of matrices. As is usually done, we describe the system's structure through a graph whose edges indicate possible nonzero entries in the system matrix. We call a graph stable if the corresponding vector space contains an open set of Hurwitz matrices. We then consider two ErdoH \s-Re'\nyi random graph models, and we obtain for each the probability that a graph sampled from these models is stable.