Exact Asymptotic Stability Analysis and Region-of-Attraction Estimation for Nonlinear Systems

We address the problem of asymptotic stability and region-of-attraction analysis of nonlinear dynamical systems. A hybrid symbolic-numeric method is presented to compute exact Lyapunov functions and exact estimates of regions of attraction of nonlinear systems efficiently. A numerical Lyapunov funct...

Full description

Saved in:
Bibliographic Details
Published in:Abstract and Applied Analysis 2013-01, Vol.2013 (2013), p.661-670
Main Authors: Wu, Min, Lin, Wang, Yang, Zhengfeng
Format: Article
Language:English
Subjects:
Dynamical systems
Liapunov functions
Linear programming
Mathematical research
Nonlinear theories
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-a558t-c2f07914238fc27c530848879efeefc9c9bfee7e00ae4da47c122b8a7381163d3
cites cdi_FETCH-LOGICAL-a558t-c2f07914238fc27c530848879efeefc9c9bfee7e00ae4da47c122b8a7381163d3
container_end_page 670
container_issue 2013
container_start_page 661
container_title Abstract and Applied Analysis
container_volume 2013
creator Wu, Min
Lin, Wang
Yang, Zhengfeng
description We address the problem of asymptotic stability and region-of-attraction analysis of nonlinear dynamical systems. A hybrid symbolic-numeric method is presented to compute exact Lyapunov functions and exact estimates of regions of attraction of nonlinear systems efficiently. A numerical Lyapunov function and an estimate of region of attraction can be obtained by solving an (bilinear) SOS programming via BMI solver, then the modified Newton refinement and rational vector recovery techniques are applied to obtain exact Lyapunov functions and verified estimates of regions of attraction with rational coefficients. Experiments on some benchmarks are given to illustrate the efficiency of our algorithm.
doi_str_mv 10.1155/2013/146137
format article
fullrecord <record><control><sourceid>gale_doaj_</sourceid><recordid>TN_cdi_doaj_primary_oai_doaj_org_article_4a414ee8c0c746fe8cf435cecb02b431</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><galeid>A369793935</galeid><airiti_id>P20160825001_201312_201609070065_201609070065_661_670</airiti_id><doaj_id>oai_doaj_org_article_4a414ee8c0c746fe8cf435cecb02b431</doaj_id><sourcerecordid>A369793935</sourcerecordid><originalsourceid>FETCH-LOGICAL-a558t-c2f07914238fc27c530848879efeefc9c9bfee7e00ae4da47c122b8a7381163d3</originalsourceid><addsrcrecordid>eNqFUcFu1DAQjRBIlMKJM1LOoLTj2I6dG9FqaSutAFF6RNasYy9eZeOV7Qry9zibVaWekA_zZvzmzdivKN4TuCKE8-saCL0mrCFUvCguSCNFBQzalxmD5BWlgr8u3sS4BwAqGLsofq3_ok5lF6fDMfnkdHmfcOsGl6ayG3GYoosljn35w-ycHytvqy6lkHtyVq5jcgc8QetD-dWPgxsNhvJ-iskc4tvilcUhmnfneFk8fFn_XN1Wm283d6tuUyHnMlW6tiBawmoqra6F5hQkk1K0xhpjdavbbQbCAKBhPTKhSV1vJQoqCWloTy-Lu0W397hXx5CXCpPy6NSp4MNOYciPG4xiyAgzRmrQgjU2A8so10Zvod4ySrLW50XrGPze6GQe9eD6Z6Krh825eg6IqAhtKSdE1jJLXC0SO8wT3Wj9_GP59ObgtB-Ndbne0aYV7dyVGz4tDTr4GIOxT-MIqNlZNTurFmcz--PC_u3GHv-4_5A_LGSTKcbiE5mxlop5181yjy645NTeP4bse1Tfs0oDsuYA5KRIanUqtSAAGv48aRqiGgH0H1NvwhI</addsrcrecordid><sourcetype>Open Website</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Exact Asymptotic Stability Analysis and Region-of-Attraction Estimation for Nonlinear Systems</title><source>Wiley-Blackwell Open Access Collection</source><source>Publicly Available Content (ProQuest)</source><creator>Wu, Min ; Lin, Wang ; Yang, Zhengfeng</creator><contributor>Camilli, Fabio M.</contributor><creatorcontrib>Wu, Min ; Lin, Wang ; Yang, Zhengfeng ; Camilli, Fabio M.</creatorcontrib><description>We address the problem of asymptotic stability and region-of-attraction analysis of nonlinear dynamical systems. A hybrid symbolic-numeric method is presented to compute exact Lyapunov functions and exact estimates of regions of attraction of nonlinear systems efficiently. A numerical Lyapunov function and an estimate of region of attraction can be obtained by solving an (bilinear) SOS programming via BMI solver, then the modified Newton refinement and rational vector recovery techniques are applied to obtain exact Lyapunov functions and verified estimates of regions of attraction with rational coefficients. Experiments on some benchmarks are given to illustrate the efficiency of our algorithm.</description><identifier>ISSN: 1085-3375</identifier><identifier>EISSN: 1687-0409</identifier><identifier>DOI: 10.1155/2013/146137</identifier><language>eng</language><publisher>Cairo, Egypt: Hindawi Limiteds</publisher><subject>Dynamical systems ; Liapunov functions ; Linear programming ; Mathematical research ; Nonlinear theories</subject><ispartof>Abstract and Applied Analysis, 2013-01, Vol.2013 (2013), p.661-670</ispartof><rights>Copyright © 2013 Min Wu et al.</rights><rights>COPYRIGHT 2013 John Wiley &amp; Sons, Inc.</rights><rights>Copyright 2013 Hindawi Publishing Corporation</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-a558t-c2f07914238fc27c530848879efeefc9c9bfee7e00ae4da47c122b8a7381163d3</citedby><cites>FETCH-LOGICAL-a558t-c2f07914238fc27c530848879efeefc9c9bfee7e00ae4da47c122b8a7381163d3</cites><orcidid>0000-0003-4467-2186</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,780,784,885,27924,27925</link.rule.ids></links><search><contributor>Camilli, Fabio M.</contributor><creatorcontrib>Wu, Min</creatorcontrib><creatorcontrib>Lin, Wang</creatorcontrib><creatorcontrib>Yang, Zhengfeng</creatorcontrib><title>Exact Asymptotic Stability Analysis and Region-of-Attraction Estimation for Nonlinear Systems</title><title>Abstract and Applied Analysis</title><description>We address the problem of asymptotic stability and region-of-attraction analysis of nonlinear dynamical systems. A hybrid symbolic-numeric method is presented to compute exact Lyapunov functions and exact estimates of regions of attraction of nonlinear systems efficiently. A numerical Lyapunov function and an estimate of region of attraction can be obtained by solving an (bilinear) SOS programming via BMI solver, then the modified Newton refinement and rational vector recovery techniques are applied to obtain exact Lyapunov functions and verified estimates of regions of attraction with rational coefficients. Experiments on some benchmarks are given to illustrate the efficiency of our algorithm.</description><subject>Dynamical systems</subject><subject>Liapunov functions</subject><subject>Linear programming</subject><subject>Mathematical research</subject><subject>Nonlinear theories</subject><issn>1085-3375</issn><issn>1687-0409</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><sourceid>DOA</sourceid><recordid>eNqFUcFu1DAQjRBIlMKJM1LOoLTj2I6dG9FqaSutAFF6RNasYy9eZeOV7Qry9zibVaWekA_zZvzmzdivKN4TuCKE8-saCL0mrCFUvCguSCNFBQzalxmD5BWlgr8u3sS4BwAqGLsofq3_ok5lF6fDMfnkdHmfcOsGl6ayG3GYoosljn35w-ycHytvqy6lkHtyVq5jcgc8QetD-dWPgxsNhvJ-iskc4tvilcUhmnfneFk8fFn_XN1Wm283d6tuUyHnMlW6tiBawmoqra6F5hQkk1K0xhpjdavbbQbCAKBhPTKhSV1vJQoqCWloTy-Lu0W397hXx5CXCpPy6NSp4MNOYciPG4xiyAgzRmrQgjU2A8so10Zvod4ySrLW50XrGPze6GQe9eD6Z6Krh825eg6IqAhtKSdE1jJLXC0SO8wT3Wj9_GP59ObgtB-Ndbne0aYV7dyVGz4tDTr4GIOxT-MIqNlZNTurFmcz--PC_u3GHv-4_5A_LGSTKcbiE5mxlop5181yjy645NTeP4bse1Tfs0oDsuYA5KRIanUqtSAAGv48aRqiGgH0H1NvwhI</recordid><startdate>20130101</startdate><enddate>20130101</enddate><creator>Wu, Min</creator><creator>Lin, Wang</creator><creator>Yang, Zhengfeng</creator><general>Hindawi Limiteds</general><general>Hindawi Puplishing Corporation</general><general>Hindawi Publishing Corporation</general><general>John Wiley &amp; Sons, Inc</general><general>Hindawi Limited</general><scope>188</scope><scope>ADJCN</scope><scope>AHFXO</scope><scope>RHU</scope><scope>RHW</scope><scope>RHX</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>DOA</scope><orcidid>https://orcid.org/0000-0003-4467-2186</orcidid></search><sort><creationdate>20130101</creationdate><title>Exact Asymptotic Stability Analysis and Region-of-Attraction Estimation for Nonlinear Systems</title><author>Wu, Min ; Lin, Wang ; Yang, Zhengfeng</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a558t-c2f07914238fc27c530848879efeefc9c9bfee7e00ae4da47c122b8a7381163d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Dynamical systems</topic><topic>Liapunov functions</topic><topic>Linear programming</topic><topic>Mathematical research</topic><topic>Nonlinear theories</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wu, Min</creatorcontrib><creatorcontrib>Lin, Wang</creatorcontrib><creatorcontrib>Yang, Zhengfeng</creatorcontrib><collection>Airiti Library</collection><collection>الدوريات العلمية والإحصائية - e-Marefa Academic and Statistical Periodicals</collection><collection>معرفة - المحتوى العربي الأكاديمي المتكامل - e-Marefa Academic Complete</collection><collection>Hindawi Publishing Complete</collection><collection>Hindawi Publishing Subscription Journals</collection><collection>Hindawi Publishing Open Access</collection><collection>CrossRef</collection><collection>DOAJ Directory of Open Access Journals</collection><jtitle>Abstract and Applied Analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wu, Min</au><au>Lin, Wang</au><au>Yang, Zhengfeng</au><au>Camilli, Fabio M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Exact Asymptotic Stability Analysis and Region-of-Attraction Estimation for Nonlinear Systems</atitle><jtitle>Abstract and Applied Analysis</jtitle><date>2013-01-01</date><risdate>2013</risdate><volume>2013</volume><issue>2013</issue><spage>661</spage><epage>670</epage><pages>661-670</pages><issn>1085-3375</issn><eissn>1687-0409</eissn><abstract>We address the problem of asymptotic stability and region-of-attraction analysis of nonlinear dynamical systems. A hybrid symbolic-numeric method is presented to compute exact Lyapunov functions and exact estimates of regions of attraction of nonlinear systems efficiently. A numerical Lyapunov function and an estimate of region of attraction can be obtained by solving an (bilinear) SOS programming via BMI solver, then the modified Newton refinement and rational vector recovery techniques are applied to obtain exact Lyapunov functions and verified estimates of regions of attraction with rational coefficients. Experiments on some benchmarks are given to illustrate the efficiency of our algorithm.</abstract><cop>Cairo, Egypt</cop><pub>Hindawi Limiteds</pub><doi>10.1155/2013/146137</doi><tpages>10</tpages><orcidid>https://orcid.org/0000-0003-4467-2186</orcidid><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 1085-3375
ispartof Abstract and Applied Analysis, 2013-01, Vol.2013 (2013), p.661-670
issn 1085-3375
1687-0409
language eng
recordid cdi_doaj_primary_oai_doaj_org_article_4a414ee8c0c746fe8cf435cecb02b431
source Wiley-Blackwell Open Access Collection; Publicly Available Content (ProQuest)
subjects Dynamical systems
Liapunov functions
Linear programming
Mathematical research
Nonlinear theories
title Exact Asymptotic Stability Analysis and Region-of-Attraction Estimation for Nonlinear Systems
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-02T18%3A43%3A38IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-gale_doaj_&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Exact%20Asymptotic%20Stability%20Analysis%20and%20Region-of-Attraction%20Estimation%20for%20Nonlinear%20Systems&rft.jtitle=Abstract%20and%20Applied%20Analysis&rft.au=Wu,%20Min&rft.date=2013-01-01&rft.volume=2013&rft.issue=2013&rft.spage=661&rft.epage=670&rft.pages=661-670&rft.issn=1085-3375&rft.eissn=1687-0409&rft_id=info:doi/10.1155/2013/146137&rft_dat=%3Cgale_doaj_%3EA369793935%3C/gale_doaj_%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-a558t-c2f07914238fc27c530848879efeefc9c9bfee7e00ae4da47c122b8a7381163d3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rft_galeid=A369793935&rft_airiti_id=P20160825001_201312_201609070065_201609070065_661_670&rfr_iscdi=true