A Kalman Decomposition for Possibly Controllable Uncertain Linear Systems

TL;DR

This paper introduces a new geometric framework for uncertain linear systems, leading to a Kalman decomposition that aids in model reduction by characterizing possibly controllable states under uncertainty.

Contribution

It provides a novel geometric characterization of possibly controllable states and a general Kalman type decomposition for uncertain systems, extending previous concepts of robust unobservability.

Findings

New geometric characterization of possibly controllable states

Kalman type decomposition for uncertain systems

Facilitates reduced order model derivation

Abstract

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.