On Structured Realizability and Stabilizability of Linear Systems
Abstract
We study the notion of structured realizability for linear systems defined over graphs. A stabilizable and detectable realization is structured if the state-space matrices inherit the sparsity pattern of the adjacency matrix of the associated graph. In this paper, we demonstrate that not every structured transfer matrix has a structured realization and we reveal the practical meaning of this fact. We also uncover a close connection between the structured realizability of a plant and whether the plant can be stabilized by a structured controller. In particular, we show that a structured stabilizing controller can only exist when the plant admits a structured realization. Finally, we give a parameterization of all structured stabilizing controllers and show that they always have structured realizations.
Keywords
Cite
@article{arxiv.1212.1839,
title = {On Structured Realizability and Stabilizability of Linear Systems},
author = {Laurent Lessard and Maxim Kristalny and Anders Rantzer},
journal= {arXiv preprint arXiv:1212.1839},
year = {2012}
}