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On Structured Realizability and Stabilizability of Linear Systems

Lessard, Laurent LU ; Kristalny, Maxim LU and Rantzer, Anders LU (2013) American Control Conference, 2013 p.5804-5810
Abstract
We study the notion of structured realizability for linear systems dened 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... (More)
We study the notion of structured realizability for linear systems dened 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. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to conference
publication status
published
subject
keywords
Realizability, Stabilizability, Linear Systems
pages
5804 - 5810
conference name
American Control Conference, 2013
external identifiers
  • Scopus:84883528527
project
LCCC
language
English
LU publication?
yes
id
5709c851-7423-4057-8181-7f3727c9a133 (old id 3994145)
date added to LUP
2013-08-26 12:07:33
date last changed
2016-10-13 05:02:07
@misc{5709c851-7423-4057-8181-7f3727c9a133,
  abstract     = {We study the notion of structured realizability for linear systems dened 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<br/><br>
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.},
  author       = {Lessard, Laurent and Kristalny, Maxim and Rantzer, Anders},
  keyword      = {Realizability,Stabilizability,Linear Systems},
  language     = {eng},
  pages        = {5804--5810},
  title        = {On Structured Realizability and Stabilizability of Linear Systems},
  year         = {2013},
}