A Kalman Decomposition for Possibly Controllable Uncertain Linear Systems

This paper considers the structure of uncertain linear systems building on concepts of robust unobservability and possible controllability which were introduced in previous papers. The paper presents a new characterization of the possibly controllable states for the case in which a certain system transfer function is non-zero. This result complements the result of a previous paper which presented a characterization of the possibly controllable states for the case in which the transfer function is zero. When combined with previous geometric results on robust unobservability and possible controllability, the results of this paper lead to a general Kalman type decomposition for uncertain linear systems.