Separable Lyapunov functions for monotone systems: Constructions and limitations.
Dirr, Gunther ; Ito, Hiroshi ; Rantzer, Anders LU
and Rüffer, Björn
(2015)
In Discrete and Continuous Dynamical Systems. Series B
20(8).
p.2497-2526
- Abstract
- For monotone systems evolving on the positive orthant, two types of Lyapunov functions are considered: Sum- and max-separable Lyapunov functions. One can be written as a sum, the other as a maximum of functions of scalar arguments. Several constructive existence results for both types are given. Notably, one construction provides a max-separable Lyapunov function that is defined at least on an arbitrarily large compact set, based on little more than the knowledge about one trajectory. Another construction for a class of planar systems yields a global sum-separable Lyapunov function, provided the right hand side satisfies a small-gain type condition. A number of examples demonstrate these methods and shed light on the relation between the... (More)
- For monotone systems evolving on the positive orthant, two types of Lyapunov functions are considered: Sum- and max-separable Lyapunov functions. One can be written as a sum, the other as a maximum of functions of scalar arguments. Several constructive existence results for both types are given. Notably, one construction provides a max-separable Lyapunov function that is defined at least on an arbitrarily large compact set, based on little more than the knowledge about one trajectory. Another construction for a class of planar systems yields a global sum-separable Lyapunov function, provided the right hand side satisfies a small-gain type condition. A number of examples demonstrate these methods and shed light on the relation between the shape of sublevel sets and the right hand side of the system equation. Negative examples show that there are indeed globally asymptotically stable systems that do not admit either type of Lyapunov function. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/7753319
- author
- Dirr, Gunther
; Ito, Hiroshi
; Rantzer, Anders
LU
and Rüffer, Björn
- organization
- publishing date
- 2015
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Discrete and Continuous Dynamical Systems. Series B
- volume
- 20
- issue
- 8
- pages
- 2497 - 2526
- publisher
- Amer Inst Mathematical Sciences
- external identifiers
-
- wos:000362747200009
- scopus:84939825936
- ISSN
- 1553-524X
- DOI
- 10.3934/dcdsb.2015.20.2497
- project
- LCCC
- language
- English
- LU publication?
- yes
- id
- 35dbbf10-7332-4c7b-af47-833575cc6fde (old id 7753319)
- date added to LUP
- 2016-04-01 09:54:20
- date last changed
- 2024-05-04 23:44:53
@article{35dbbf10-7332-4c7b-af47-833575cc6fde,
abstract = {{For monotone systems evolving on the positive orthant, two types of Lyapunov functions are considered: Sum- and max-separable Lyapunov functions. One can be written as a sum, the other as a maximum of functions of scalar arguments. Several constructive existence results for both types are given. Notably, one construction provides a max-separable Lyapunov function that is defined at least on an arbitrarily large compact set, based on little more than the knowledge about one trajectory. Another construction for a class of planar systems yields a global sum-separable Lyapunov function, provided the right hand side satisfies a small-gain type condition. A number of examples demonstrate these methods and shed light on the relation between the shape of sublevel sets and the right hand side of the system equation. Negative examples show that there are indeed globally asymptotically stable systems that do not admit either type of Lyapunov function.}},
author = {{Dirr, Gunther and Ito, Hiroshi and Rantzer, Anders and Rüffer, Björn}},
issn = {{1553-524X}},
language = {{eng}},
number = {{8}},
pages = {{2497--2526}},
publisher = {{Amer Inst Mathematical Sciences}},
series = {{Discrete and Continuous Dynamical Systems. Series B}},
title = {{Separable Lyapunov functions for monotone systems: Constructions and limitations.}},
url = {{https://lup.lub.lu.se/search/files/1376296/8229290.pdf}},
doi = {{10.3934/dcdsb.2015.20.2497}},
volume = {{20}},
year = {{2015}},
}