A Kalman Decomposition for Robustly Unobservable Uncertain Linear Systems

This paper considers the structure of uncertain linear systems building on a concept of robust unobservability which was introduced in a previous paper. Compared to the previous paper, this paper specializes to the case of linear time invariant uncertain systems with unstructured uncertainty described by an averaged integral quadratic constraint. The paper presents a new characterization of the robustly unobservable states and shows that this leads to a Kalman type decomposition for uncertain linear systems with robustly unobservable states.