Advanced

A Tutorial on Positive Systems and Large Scale Control

Rantzer, Anders LU and Valcher, Maria Elena (2019) 57th IEEE Conference on Decision and Control p.3686-3697
Abstract
In this tutorial paper we first present some foundational results regarding the theory of positive systems. In particular, we present fundamental results regarding stability, positive realization and positive stabilization by means of state feedback. Special attention is also paid to the system performance in terms of disturbance attenuation. Under the asymptotic stability assumption, such performance can be measured in terms of Lp-gain of the positive system. In the second part of the paper we propose some recent results about control synthesis by linear programming and semi-definite programming, under the positivity requirement on the resulting controlled system. These results highlight the value of positivity when dealing with large... (More)
In this tutorial paper we first present some foundational results regarding the theory of positive systems. In particular, we present fundamental results regarding stability, positive realization and positive stabilization by means of state feedback. Special attention is also paid to the system performance in terms of disturbance attenuation. Under the asymptotic stability assumption, such performance can be measured in terms of Lp-gain of the positive system. In the second part of the paper we propose some recent results about control synthesis by linear programming and semi-definite programming, under the positivity requirement on the resulting controlled system. These results highlight the value of positivity when dealing with large scale systems. Indeed, stability properties for these systems can be verified by resorting to linear (copositive) or diagonal Lyapunov functions that scale linearly with the system dimension, and such linear functions can be used also to design stabilizing feedback control laws. In addition, stabilization problems with disturbance attenuation performance can be easily solved by imposing special structures on the state feedback matrices. This is extremely valuable when dealing with large scale systems for which state feedback matrices are typically sparse, and their structure is a priori imposed by practical requirements. (Less)
Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
Proceedings IEEE Conference on Decision and Control
pages
12 pages
publisher
Institute of Electrical and Electronics Engineers Inc.
conference name
57th IEEE Conference on Decision and Control
conference location
Miami Beach, United States
conference dates
2018-12-17 - 2018-12-19
external identifiers
  • scopus:85062182997
ISBN
978-1-5386-1395-5
DOI
10.1109/CDC.2018.8618689
project
LCCC
language
English
LU publication?
yes
id
8c599386-10ac-4265-aa5a-9d3d2658197a
date added to LUP
2019-02-01 16:08:15
date last changed
2020-09-27 07:04:10
@inproceedings{8c599386-10ac-4265-aa5a-9d3d2658197a,
  abstract     = {In this tutorial paper we first present some foundational results regarding the theory of positive systems. In particular, we present fundamental results regarding stability, positive realization and positive stabilization by means of state feedback. Special attention is also paid to the system performance in terms of disturbance attenuation. Under the asymptotic stability assumption, such performance can be measured in terms of Lp-gain of the positive system. In the second part of the paper we propose some recent results about control synthesis by linear programming and semi-definite programming, under the positivity requirement on the resulting controlled system. These results highlight the value of positivity when dealing with large scale systems. Indeed, stability properties for these systems can be verified by resorting to linear (copositive) or diagonal Lyapunov functions that scale linearly with the system dimension, and such linear functions can be used also to design stabilizing feedback control laws. In addition, stabilization problems with disturbance attenuation performance can be easily solved by imposing special structures on the state feedback matrices. This is extremely valuable when dealing with large scale systems for which state feedback matrices are typically sparse, and their structure is a priori imposed by practical requirements.},
  author       = {Rantzer, Anders and Valcher, Maria Elena},
  booktitle    = {Proceedings IEEE Conference on Decision and Control},
  isbn         = {978-1-5386-1395-5},
  language     = {eng},
  pages        = {3686--3697},
  publisher    = {Institute of Electrical and Electronics Engineers Inc.},
  title        = {A Tutorial on Positive Systems and Large Scale Control},
  url          = {http://dx.doi.org/10.1109/CDC.2018.8618689},
  doi          = {10.1109/CDC.2018.8618689},
  year         = {2019},
}