A Kalman Decomposition for Possibly Controllable Uncertain Linear Systems
For control theorists, this extends structural decomposition to uncertain systems, but it is an incremental extension of prior work on robust unobservability.
The paper provides a geometric characterization of possibly controllable states for uncertain linear systems, leading to a Kalman-type decomposition that enables reduced-order modeling.
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 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.