On the stability of uncertain stochastic systems in Hilbert space

Abstract

In this paper, we present some new results on the robustness of linear infinite-dimensional stochastic systems.
As a robustness metric, we use the concept of stability radius. First, we investigate the robustness of
stability in the presence of stochastic structured perturbations. We provide characterizations for the
stability radius. These are obtained via stochastic Lyapunov equation and the corresponding inequalities.
Then, we consider the maximization of the stability radius by state feedback.