Uniting Two Control Lyapunov Functions for Affine Systems
The problem of piecing together two control Lyapunov functions (CLFs) is addressed. The first CLF characterizes a local asymptotic controllability property toward the origin, whereas the second CLF is related to a global asymptotic controllability property with respect to a compact set. A sufficient...
Saved in:
| Published in | 2008 47th IEEE Conference on Decision and Control Vol. 55; no. 8; pp. 1923 - 1927 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York, NY
IEEE
01.08.2010
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0018-9286 1558-2523 |
| DOI | 10.1109/TAC.2010.2049689 |
Cover
| Abstract | The problem of piecing together two control Lyapunov functions (CLFs) is addressed. The first CLF characterizes a local asymptotic controllability property toward the origin, whereas the second CLF is related to a global asymptotic controllability property with respect to a compact set. A sufficient condition is expressed to obtain an explicit solution. This sufficient condition is shown to be always satisfied for a linear second order controllable system. In a second part, it is shown how this uniting CLF problem can be used to solve the problem of piecing together two stabilizing control laws. Finally, this framework is applied on a numerical example to improve local performance of a globally stabilizing state feedback. |
|---|---|
| AbstractList | The problem of piecing together two control Lyapunov functions (CLFs) is addressed. The first CLF characterizes a local asymptotic controllability property toward the origin, whereas the second CLF is related to a global asymptotic controllability property with respect to a compact set. A sufficient condition is expressed to obtain an explicit solution. This sufficient condition is shown to be always satisfied for a linear second order controllable system. In a second part, it is shown how this uniting CLF problem can be used to solve the problem of piecing together two stabilizing control laws. Finally, this framework is applied on a numerical example to improve local performance of a globally stabilizing state feedback. The problem of piecing together two Control Lyapunov Functions (CLFs) is addressed. The first CLF characterizes a local asymptotic controllability property toward the origin, whereas the second CLF is related to a global asymptotic controllability property with respect to a compact set. A sufficient condition is expressed to obtain an explicit solution. This sufficient condition is shown to be always satisfied for a linear second order controllable system. In a second part, it is shown how this uniting CLF problem can be used to solve the problem of piecing together two stabilizing control laws. Finally, this framework is applied on a numerical example to improve local performance of a globally stabilizing state feedback. Note that this paper is the full version of a paper submitted to IEEE TAC. |
| Author | Prieur, C Andrieu, V |
| Author_xml | – sequence: 1 givenname: V surname: Andrieu fullname: Andrieu, V email: vincent.andrieu@gmail.com organization: Univ. de Lyon, Lyon, France – sequence: 2 givenname: C surname: Prieur fullname: Prieur, C email: cprieur@laas.fr organization: CNRS-LAAS, Toulouse, France |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=23090436$$DView record in Pascal Francis https://hal.science/hal-00432607$$DView record in HAL |
| BookMark | eNp9kc-LEzEUx4OsYLd6F7wMiIiHWfN7kmMprisUPNg9h9dMRrNMk5pkdul_b8qUFSoIgfDC55v3PrxrdBVicAi9JfiGEKw_b1frG4prRTHXUukXaEGEUC0VlF2hBcZEtZoq-Qpd5_xQS8k5WSB9H3zx4WezfYrNOoaS4thsjnCYQnxsbqdgi48hN0NMzWoYfHDNj2Mubp9fo5cDjNm9Od9LdH_7Zbu-azffv35brzat5VSXlgy7HQCT3OmeCS6pVRi4prjjcscUyEH2jvDeQa90FdlhrkTPqei1lUT0bInI_O8UDnB8gnE0h-T3kI6GYHNyNwWsObmbs3vNfJozv-AvHcGbu9XGnN4w5oxK3D3Syn6c2UOKvyeXi9n7bN04QnBxyqZTHWWE1bNE7y_IhzilUOXrJLTrOi0pr9SHMwXZwjgkCNbn5ykow7o2l5XDM2dTzDm54R-tutJLLXkRsb7AaUElgR__F3w3B71z7rmP4EJVgP0BjL6qvQ |
| CODEN | IETAA9 |
| CitedBy_id | crossref_primary_10_1016_j_automatica_2013_03_009 crossref_primary_10_4236_jamp_2023_114069 crossref_primary_10_1016_j_sysconle_2011_04_015 crossref_primary_10_3182_20140824_6_ZA_1003_01513 crossref_primary_10_1016_j_automatica_2015_12_011 crossref_primary_10_1016_j_automatica_2014_10_019 crossref_primary_10_1002_rnc_7360 crossref_primary_10_1016_j_arcontrol_2011_03_001 crossref_primary_10_1016_j_automatica_2012_06_099 crossref_primary_10_1109_TAC_2012_2229842 crossref_primary_10_1142_S0218127424500895 crossref_primary_10_1109_TAC_2017_2668380 crossref_primary_10_1080_00207179_2021_2024604 crossref_primary_10_1016_j_jfranklin_2024_106692 crossref_primary_10_1109_TAC_2013_2281479 crossref_primary_10_1109_TAC_2015_2495231 crossref_primary_10_1002_rnc_1668 crossref_primary_10_3182_20130904_3_FR_2041_00026 crossref_primary_10_1080_00207179_2011_641159 crossref_primary_10_1109_LCSYS_2022_3226881 crossref_primary_10_1109_TAC_2013_2277632 crossref_primary_10_1016_j_automatica_2014_12_017 crossref_primary_10_1016_j_automatica_2017_10_005 crossref_primary_10_1109_TAC_2013_2263613 crossref_primary_10_3182_20110828_6_IT_1002_00227 |
| Cites_doi | 10.1109/CDC.2008.4739481 10.1137/S0363012993258732 10.1109/ACC.1997.610803 10.1137/060675861 10.1137/050642629 10.1109/9.543995 10.1137/S0363012901391676 10.1007/PL00009880 10.1109/CDC.2007.4434383 10.1007/978-1-4471-0967-9 10.1109/9.935055 10.1080/10556789908805766 10.1016/0167-6911(91)90111-Q 10.1016/0362-546X(83)90049-4 |
| ContentType | Journal Article |
| Copyright | 2015 INIST-CNRS Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Aug 2010 Distributed under a Creative Commons Attribution 4.0 International License |
| Copyright_xml | – notice: 2015 INIST-CNRS – notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Aug 2010 – notice: Distributed under a Creative Commons Attribution 4.0 International License |
| DBID | 97E RIA RIE AAYXX CITATION IQODW 7SC 7SP 7TB 8FD FR3 JQ2 L7M L~C L~D F28 1XC VOOES ADTOC UNPAY |
| DOI | 10.1109/TAC.2010.2049689 |
| DatabaseName | IEEE All-Society Periodicals Package (ASPP) 2005–Present IEEE All-Society Periodicals Package (ASPP) 1998–Present IEEE Electronic Library (IEL) CrossRef Pascal-Francis Computer and Information Systems Abstracts Electronics & Communications Abstracts Mechanical & Transportation Engineering Abstracts Technology Research Database Engineering Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional ANTE: Abstracts in New Technology & Engineering Hyper Article en Ligne (HAL) Hyper Article en Ligne (HAL) (Open Access) Unpaywall for CDI: Periodical Content Unpaywall |
| DatabaseTitle | CrossRef Technology Research Database Computer and Information Systems Abstracts – Academic Mechanical & Transportation Engineering Abstracts Electronics & Communications Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Engineering Research Database Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional ANTE: Abstracts in New Technology & Engineering |
| DatabaseTitleList | Technology Research Database Technology Research Database |
| Database_xml | – sequence: 1 dbid: RIE name: IEEE Electronic Library (IEL) url: https://proxy.k.utb.cz/login?url=https://ieeexplore.ieee.org/ sourceTypes: Publisher – sequence: 2 dbid: UNPAY name: Unpaywall url: https://proxy.k.utb.cz/login?url=https://unpaywall.org/ sourceTypes: Open Access Repository |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Applied Sciences |
| EISSN | 1558-2523 |
| EndPage | 1927 |
| ExternalDocumentID | oai:HAL:hal-00457825v1 oai_HAL_hal_00432607v2 2720471971 23090436 10_1109_TAC_2010_2049689 5458049 |
| Genre | orig-research |
| GroupedDBID | -~X .DC 0R~ 29I 3EH 4.4 5GY 5VS 6IK 97E AAJGR AARMG AASAJ AAWTH ABAZT ABQJQ ABVLG ACGFO ACGFS ACIWK ACNCT AENEX AETIX AGQYO AGSQL AHBIQ AI. AIBXA AKJIK AKQYR ALLEH ALMA_UNASSIGNED_HOLDINGS ASUFR ATWAV BEFXN BFFAM BGNUA BKEBE BPEOZ CS3 DU5 EBS EJD F5P HZ~ H~9 IAAWW IBMZZ ICLAB IDIHD IFIPE IFJZH IPLJI JAVBF LAI M43 MS~ O9- OCL P2P RIA RIE RNS TAE TN5 VH1 VJK ~02 AAYXX CITATION IQODW RIG 7SC 7SP 7TB 8FD FR3 JQ2 L7M L~C L~D F28 1XC VOOES ADTOC UNPAY |
| ID | FETCH-LOGICAL-c429t-1fbbaa364e9d35462c80a4920746b38a6f6de14dead89109b0485d425d9c615d3 |
| IEDL.DBID | RIE |
| ISSN | 0018-9286 |
| IngestDate | Mon Sep 22 05:42:56 EDT 2025 Fri Sep 12 12:40:44 EDT 2025 Wed Oct 01 00:23:43 EDT 2025 Mon Jun 30 10:14:45 EDT 2025 Mon Jul 21 09:17:37 EDT 2025 Thu Apr 24 23:01:10 EDT 2025 Wed Oct 01 01:53:35 EDT 2025 Wed Aug 27 02:48:54 EDT 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 8 |
| Keywords | State feedback Second order equation Compact space uniting problems Control program Lyapunov stabilization Non linear control Non linear system Affine transformation nonlinear systems Optimal control Global stabilization Controllability Asymptotic approximation Lyapunov function Uniting Lyapunov design Stabilization |
| Language | English |
| License | https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html CC BY 4.0 Distributed under a Creative Commons Attribution 4.0 International License: http://creativecommons.org/licenses/by/4.0 other-oa |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c429t-1fbbaa364e9d35462c80a4920746b38a6f6de14dead89109b0485d425d9c615d3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 ObjectType-Article-2 ObjectType-Feature-1 content type line 23 |
| ORCID | 0000-0002-4456-2019 0000-0003-1877-6205 |
| OpenAccessLink | https://proxy.k.utb.cz/login?url=https://hal.science/hal-00457825 |
| PQID | 1027779624 |
| PQPubID | 85475 |
| PageCount | 5 |
| ParticipantIDs | ieee_primary_5458049 crossref_primary_10_1109_TAC_2010_2049689 pascalfrancis_primary_23090436 unpaywall_primary_10_1109_tac_2010_2049689 proquest_journals_1027779624 hal_primary_oai_HAL_hal_00432607v2 proquest_miscellaneous_787231331 crossref_citationtrail_10_1109_TAC_2010_2049689 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2010-08-01 |
| PublicationDateYYYYMMDD | 2010-08-01 |
| PublicationDate_xml | – month: 08 year: 2010 text: 2010-08-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | New York, NY |
| PublicationPlace_xml | – name: New York, NY – name: New York |
| PublicationTitle | 2008 47th IEEE Conference on Decision and Control |
| PublicationTitleAbbrev | TAC |
| PublicationYear | 2010 |
| Publisher | IEEE Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher_xml | – name: IEEE – name: Institute of Electrical and Electronics Engineers – name: The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| References | ref13 ref12 ref15 ref11 ref10 ref2 ref1 sepulchre (ref14) 1997 ref17 ref16 ref7 ref9 ref4 ref5 krstic (ref6) 1995 andrieu (ref3) 2009 lfberg (ref8) 2004 |
| References_xml | – ident: ref13 doi: 10.1109/CDC.2008.4739481 – ident: ref5 doi: 10.1137/S0363012993258732 – ident: ref16 doi: 10.1109/ACC.1997.610803 – ident: ref2 doi: 10.1137/060675861 – ident: ref12 doi: 10.1137/050642629 – ident: ref9 doi: 10.1109/9.543995 – ident: ref1 doi: 10.1137/S0363012901391676 – year: 1995 ident: ref6 publication-title: Nonlinear and Adaptive Control Design – ident: ref11 doi: 10.1007/PL00009880 – ident: ref17 doi: 10.1109/CDC.2007.4434383 – year: 1997 ident: ref14 publication-title: Constructive Nonlinear Control doi: 10.1007/978-1-4471-0967-9 – ident: ref10 doi: 10.1109/9.935055 – year: 2004 ident: ref8 article-title: Yalmip: A toolbox for modeling and optimization in MATLAB publication-title: Proc CACSD Conf – ident: ref15 doi: 10.1080/10556789908805766 – year: 2009 ident: ref3 publication-title: Uniting Two Control Lyapunov Functions for Affine Systems (Full Version) – ident: ref7 doi: 10.1016/0167-6911(91)90111-Q – ident: ref4 doi: 10.1016/0362-546X(83)90049-4 |
| SSID | ssj0016441 |
| Score | 2.2030385 |
| Snippet | The problem of piecing together two control Lyapunov functions (CLFs) is addressed. The first CLF characterizes a local asymptotic controllability property... The problem of piecing together two Control Lyapunov Functions (CLFs) is addressed. The first CLF characterizes a local asymptotic controllability property... |
| SourceID | unpaywall hal proquest pascalfrancis crossref ieee |
| SourceType | Open Access Repository Aggregation Database Index Database Enrichment Source Publisher |
| StartPage | 1923 |
| SubjectTerms | Applied sciences Asymptotic properties Automatic Automatic control Computer science; control theory; systems Control system analysis Control system synthesis Control systems Control theory. Systems Controllability Engineering Sciences Exact sciences and technology Feedback control Instruments Lyapunov functions Lyapunov method Lyapunov stabilization Mathematical models Modelling and identification Nonlinear control systems Nonlinear systems Optimal control Origins Stability State feedback Sufficient conditions uniting problems |
| SummonAdditionalLinks | – databaseName: Unpaywall dbid: UNPAY link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1Na9wwEB2SzaG59IO0xEkaROklBSf-kGXraJYuS0lDD7uQnIwkSwS6eJesvSH99ZmxvSbbQqA3Y0kgaWY8T-j5DcBX7mzoAut8Gxjh84xHvnYq8UuF2TRNdGxabs7PGzGd8x-3ye0esO2_MPeIOPtvPz37BDkwiSX7cCDoCmkEB_ObX_nd9sYxkFe1Mh1FK0K0K6he-4sMs39P_Ma2cArRHtUaV-66khU7mPJNU63U06NaLF6kl8m7jua4blUJiVXy-7Kp9aX585dm42szfw9ve2zJ8s4ZPsCerY5AEqrE_MRmj0s27ojp7PpJrZpquWETTGut5zEEryx3DkEn61XMP8J88n02nvp9vQTfYFap_dBprVQsuJVlnHARmSxQXEZUUkTHmRJOlDbkJTpPhihBaozepMSgLaVBYFPGn2BULSt7DCwpQ8zc2gojcUCaKYxrobNAK0t6NdaDq-0eF6YXE6eaFouiPVQEspjl44KsUvRW8eBiGLHqhDRe6fsFd3DoRgrY0_y6oHethKAI0k3kwRFZdehFN4A43IPzHSsP7XjWkqS378HZ1uxFH69rnEmUpqkUEfeADc0YaXR9oiq7bNYFbgGC4TgOPfg2eMs_a0Fv3FnLyf90PoXDjp1ABMMzGNUPjf2MoKfW573fPwPlZfvn priority: 102 providerName: Unpaywall |
| Title | Uniting Two Control Lyapunov Functions for Affine Systems |
| URI | https://ieeexplore.ieee.org/document/5458049 https://www.proquest.com/docview/1027779624 https://www.proquest.com/docview/787231331 https://hal.science/hal-00432607 https://hal.science/hal-00457825 |
| UnpaywallVersion | submittedVersion |
| Volume | 55 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVIEE databaseName: IEEE Electronic Library (IEL) customDbUrl: eissn: 1558-2523 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0016441 issn: 0018-9286 databaseCode: RIE dateStart: 19630101 isFulltext: true titleUrlDefault: https://ieeexplore.ieee.org/ providerName: IEEE |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV3fa9swED6a7mHbw351Zd7aIMZeNubEP2TZejRhIYy27CGB7slIssRgwQ6N3dL99TvZjki2MfpmYgkk3Z3vc-7zdwAfqNGhCbTxdaCYTzMa-dKIxC8FZtM0kbHquDmXV2yxol-vk-sj-Oy-hdFad-QzPbGXXS2_rFVr_yqb2iIPItoRjNKU999quYqBzev9UxcDOMpcSTLg02U-6zlcEU5mtqH7Xgoa_bAEyK6ziuVFii0ejel7WhyAzsdttRH3d2K93ss_8-dwuVt5Tzv5OWkbOVG__hB1fOjWXsCzAYiSvPecl3Ckq1fwdE-e8AS4BaR4RZZ3NZn1nHZycS82bVXfkjlmxM5pCeJekhuDE8kggP4aVvMvy9nCH1ot-AoTUuOHRkohYkY1L-OEskhlgaA8st1IZJwJZlipQ1qi32UIMLjEwE9KjPeSK8REZXwKx1Vd6TdAkjLEpC81UxwnpJnARwKTWSCFtlI32oPp7vQLNeiQ23YY66J7Hwl4gfYqrL2KwV4efHQzNr0Gx3_GvkeDumFWPHuRXxT2t059kAXpbeTBibWAGzUcvgfjA_u7-_iaxq1UvwdnO4cohlDf4kqiFN2RRdQD4m5jkNrKi6h03W4LPALE0XEcevDJ-dFfe2mEOtjL238v8x086SkMloV4BsfNTavPERk1ctyFxBgera6-5d9_A63rCC4 |
| linkProvider | IEEE |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV1Lj9MwEB7tLoeFA68FEVgWC3EBkTYPx4mPVUVVoN1TV9pb5FeERJVUNNnV8usZx6nVAkLcotiWbM-M53Nm8g3AO1qZuIpMFZpIsZAWNAllJbJQC_SmeSZT1efmLC_Z_Ip-uc6uj-Cj_xfGGNMnn5mRfexj-bpRnf1UNrZBHkS0x3Avw1tF7v7W8jED69nduYsmnBQ-KBnx8WoydVlcCQ5ntqT7nhM6_mZTIPvaKjYzUmxxcypX1eIAdp529Ubc3Yr1es8DzR7Bcjd3l3jyfdS1cqR-_kbr-L-LewwPByhKJk53nsCRqZ_Cgz2CwjPgFpLiE1ndNmTqstrJ4k5surq5ITP0ib3aEkS-ZFJVOJAMFOjP4Gr2aTWdh0OxhVChS2rDuJJSiJRRw3WaUZaoIhKUJ7YeiUwLwSqmTUw1al6BEINLNP1Mo8VrrhAV6fQ5nNRNbV4AyXSMbl8apjgOyAuBhwKTRSSFsWQ3JoDxbvdLNTCR24IY67K_kUS8RHmVVl7lIK8A3vsRG8fC8Y--b1Ggvpulz55PFqV91_MPsii_SQI4sxLwvYbND-DiQP6-HS9q3JL1B3C-U4hyMPYtziTJ85yzhAZAfDOaqY29iNo03bbELUAknaZxAB-8Hv2xllaog7W8_Ps038DpfLVclIvPl19fwX2X0GBzEs_hpP3RmdeIk1p50ZvHL2G8Cc8 |
| linkToUnpaywall | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1Na9wwEB2SzaG59IO0xEkaROklBSf-kGXraJYuS0lDD7uQnIwkSwS6eJesvSH99ZmxvSbbQqA3Y0kgaWY8T-j5DcBX7mzoAut8Gxjh84xHvnYq8UuF2TRNdGxabs7PGzGd8x-3ye0esO2_MPeIOPtvPz37BDkwiSX7cCDoCmkEB_ObX_nd9sYxkFe1Mh1FK0K0K6he-4sMs39P_Ma2cArRHtUaV-66khU7mPJNU63U06NaLF6kl8m7jua4blUJiVXy-7Kp9aX585dm42szfw9ve2zJ8s4ZPsCerY5AEqrE_MRmj0s27ojp7PpJrZpquWETTGut5zEEryx3DkEn61XMP8J88n02nvp9vQTfYFap_dBprVQsuJVlnHARmSxQXEZUUkTHmRJOlDbkJTpPhihBaozepMSgLaVBYFPGn2BULSt7DCwpQ8zc2gojcUCaKYxrobNAK0t6NdaDq-0eF6YXE6eaFouiPVQEspjl44KsUvRW8eBiGLHqhDRe6fsFd3DoRgrY0_y6oHethKAI0k3kwRFZdehFN4A43IPzHSsP7XjWkqS378HZ1uxFH69rnEmUpqkUEfeADc0YaXR9oiq7bNYFbgGC4TgOPfg2eMs_a0Fv3FnLyf90PoXDjp1ABMMzGNUPjf2MoKfW573fPwPlZfvn |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Uniting+Two+Control+Lyapunov+Functions+for+Affine+Systems&rft.jtitle=IEEE+transactions+on+automatic+control&rft.au=Andrieu%2C+V&rft.au=Prieur%2C+C&rft.date=2010-08-01&rft.pub=IEEE&rft.issn=0018-9286&rft.volume=55&rft.issue=8&rft.spage=1923&rft.epage=1927&rft_id=info:doi/10.1109%2FTAC.2010.2049689&rft.externalDocID=5458049 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0018-9286&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0018-9286&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0018-9286&client=summon |