The issue of robustness of stability has been prominent in the literature on control theory over the last two decades. An important state-space approach to robustness analysis is the stability radii theory. The robust stability problems of infinite dimensional systems subjected to stochastic bounded structured perturbations have been studied using the stability radius approach. In the applications it is important to study these problems in the case where the perturbations operator structure are unbounded, because it covers the case of partial differential equations with boundary and ...