A. Alavian and M.C. Rotkowitz
On a Hankel-based Measure of Decentralized Controllability and Observability
Proceedings of the 5th IFAC Workshop on Distributed Estimation and Control in Networked Systems,
September 2015.

Abstract

This paper discusses the controllability of linear time-invariant (LTI) systems with decentralized controllers. Whether an LTI system is controllable (by LTI controllers) with respect to a given information structure can be determined by testing for fixed modes. Measures have been developed to further determine how far a system is from having a fixed mode, but these measures cannot actually be computed in most cases. We thus seek an easily computable, non-binary measure of controllability for LTI systems with decentralized controllers of arbitrary information structure. We develop a measure based on the Hankel operator, that combines the controllability gramian, the observability gramian, and a version of the cross-gramian which incorporates the information structure.