Separable Lyapunov functions for monotone systems: Constructions and limitations.
(2015) In Discrete and Continuous Dynamical Systems. Series B 20(8). p.24972526 Abstract
 For monotone systems evolving on the positive orthant, two types of Lyapunov functions are considered: Sum and maxseparable 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 maxseparable 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 sumseparable Lyapunov function, provided the right hand side satisfies a smallgain 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 maxseparable 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 maxseparable 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 sumseparable Lyapunov function, provided the right hand side satisfies a smallgain 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:
http://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
 1553524X
 DOI
 10.3934/dcdsb.2015.20.2497
 project
 LCCC
 language
 English
 LU publication?
 yes
 id
 35dbbf1073324c7baf47833575cc6fde (old id 7753319)
 date added to LUP
 20150805 11:03:48
 date last changed
 20180529 10:57:32
@article{35dbbf1073324c7baf47833575cc6fde, abstract = {For monotone systems evolving on the positive orthant, two types of Lyapunov functions are considered: Sum and maxseparable 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 maxseparable 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 sumseparable Lyapunov function, provided the right hand side satisfies a smallgain 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 = {1553524X}, language = {eng}, number = {8}, pages = {24972526}, publisher = {Amer Inst Mathematical Sciences}, series = {Discrete and Continuous Dynamical Systems. Series B}, title = {Separable Lyapunov functions for monotone systems: Constructions and limitations.}, url = {http://dx.doi.org/10.3934/dcdsb.2015.20.2497}, volume = {20}, year = {2015}, }