Advanced

Separable Lyapunov functions for monotone systems

Rantzer, Anders LU ; Rüffer, Björn and Dirr, Gunther (2013) 52nd IEEE Conference on Decision and Control, 2013 In [Host publication title missing]
Abstract
Separable Lyapunov functions play vital roles, for example, in stability analysis of large-scale systems. A Lyapunov function is called max-separable if it can be decomposed into a maximum of functions with one-dimensional arguments. Similarly, it is called sum-separable if it is a sum of such functions. In this paper it is shown that for a monotone system on a compact state space, asymptotic stability implies existence of a max-separable Lyapunov function. We also construct two systems on a non-compact state space, for which a max- separable Lyapunov function does not exist. One of them has a sum-separable Lyapunov function. The other does not.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
stability, Lyapunov functions, monotone systems
in
[Host publication title missing]
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
conference name
52nd IEEE Conference on Decision and Control, 2013
external identifiers
  • Scopus:84902322013
project
LCCC
language
English
LU publication?
yes
id
115b002b-100b-40c5-abd8-d8cd71c3ad0e (old id 4360464)
date added to LUP
2014-03-30 14:19:11
date last changed
2016-10-13 04:37:16
@misc{115b002b-100b-40c5-abd8-d8cd71c3ad0e,
  abstract     = {Separable Lyapunov functions play vital roles, for example, in stability analysis of large-scale systems. A Lyapunov function is called max-separable if it can be decomposed into a maximum of functions with one-dimensional arguments. Similarly, it is called sum-separable if it is a sum of such functions. In this paper it is shown that for a monotone system on a compact state space, asymptotic stability implies existence of a max-separable Lyapunov function. We also construct two systems on a non-compact state space, for which a max- separable Lyapunov function does not exist. One of them has a sum-separable Lyapunov function. The other does not.},
  author       = {Rantzer, Anders and Rüffer, Björn and Dirr, Gunther},
  keyword      = {stability,Lyapunov functions,monotone systems},
  language     = {eng},
  publisher    = {ARRAY(0xaf1a320)},
  series       = {[Host publication title missing]},
  title        = {Separable Lyapunov functions for monotone systems},
  year         = {2013},
}