This paper considers the structure of uncertain linear systems building on concepts of robust unobservability and possible controllability. The paper presents a new geometric characterization of the possibly controllable states. When combined with previous geometric results on robust unobservability, the results of this paper lead to a general Kalman type decomposition for uncertain linear systems which can be applied to the problem of obtaining reduced order uncertain system models. (C) 2013 Elsevier Ltd. All rights reserved.