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:
https://lup.lub.lu.se/record/8c599386-10ac-4265-aa5a-9d3d2658197a
- author
- Rantzer, Anders
LU
and Valcher, Maria Elena
- organization
- publishing date
- 2019
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- Proceedings IEEE Conference on Decision and Control
- pages
- 12 pages
- publisher
- IEEE - 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
- 2023-11-18 13:35:29
@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 = {{IEEE - 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}},
}