Local implications of almost global stability
Resumen:
We prove that for autonomous differential equations with the origin as a fixed point, and with at least one eigenvalue with negative real part, we have that the existence of a density function implies local asymptotical stability. We present examples of a system admitting a density function for which the origin is not locally asymptotically stable and an almost globally stable system for which no function is a density function. Keywords: nonlinear systems, asymptotical stability, density functions, almost global stability
nbsp,
| 2009 | |
|
Nonlinear systems Asymptotical stability Density functions Almost global stability |
|
| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/38675 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| _version_ | 1807522934185525248 |
|---|---|
| author | Potrie, Rafael |
| author2 | Monzón, Pablo |
| author2_role | author |
| author_facet | Potrie, Rafael Monzón, Pablo |
| author_role | author |
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| collection | COLIBRI |
| dc.creator.none.fl_str_mv | Potrie, Rafael Monzón, Pablo |
| dc.date.accessioned.none.fl_str_mv | 2023-08-01T20:33:17Z |
| dc.date.available.none.fl_str_mv | 2023-08-01T20:33:17Z |
| dc.date.issued.es.fl_str_mv | 2009 |
| dc.date.submitted.es.fl_str_mv | 20230801 |
| dc.description.abstract.none.fl_txt_mv | We prove that for autonomous differential equations with the origin as a fixed point, and with at least one eigenvalue with negative real part, we have that the existence of a density function implies local asymptotical stability. We present examples of a system admitting a density function for which the origin is not locally asymptotically stable and an almost globally stable system for which no function is a density function. Keywords: nonlinear systems, asymptotical stability, density functions, almost global stability nbsp, |
| dc.identifier.citation.es.fl_str_mv | Potrie, R., Monzón, P. Local implications of almost global stability [Preprint] Publicado en Dynamical Systems, 2009, v. 24, no. 1, doi: 10.1080/14689360802474657 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/38675 |
| dc.language.iso.none.fl_str_mv | en eng |
| dc.rights.license.none.fl_str_mv | Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| dc.rights.none.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.source.none.fl_str_mv | reponame:COLIBRI instname:Universidad de la República instacron:Universidad de la República |
| dc.subject.es.fl_str_mv | Nonlinear systems Asymptotical stability Density functions Almost global stability |
| dc.title.none.fl_str_mv | Local implications of almost global stability |
| dc.type.es.fl_str_mv | Preprint |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/preprint |
| dc.type.version.none.fl_str_mv | info:eu-repo/semantics/submittedVersion |
| description | We prove that for autonomous differential equations with the origin as a fixed point, and with at least one eigenvalue with negative real part, we have that the existence of a density function implies local asymptotical stability. We present examples of a system admitting a density function for which the origin is not locally asymptotically stable and an almost globally stable system for which no function is a density function. Keywords: nonlinear systems, asymptotical stability, density functions, almost global stability |
| eu_rights_str_mv | openAccess |
| format | preprint |
| id | COLIBRI_62ad13e4b527df706d8eadc6a27b75ee |
| identifier_str_mv | Potrie, R., Monzón, P. Local implications of almost global stability [Preprint] Publicado en Dynamical Systems, 2009, v. 24, no. 1, doi: 10.1080/14689360802474657 |
| instacron_str | Universidad de la República |
| institution | Universidad de la República |
| instname_str | Universidad de la República |
| language | eng |
| language_invalid_str_mv | en |
| network_acronym_str | COLIBRI |
| network_name_str | COLIBRI |
| oai_identifier_str | oai:colibri.udelar.edu.uy:20.500.12008/38675 |
| publishDate | 2009 |
| reponame_str | COLIBRI |
| repository.mail.fl_str_mv | mabel.seroubian@seciu.edu.uy |
| repository.name.fl_str_mv | COLIBRI - Universidad de la República |
| repository_id_str | 4771 |
| rights_invalid_str_mv | Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| spelling | 2023-08-01T20:33:17Z2023-08-01T20:33:17Z200920230801Potrie, R., Monzón, P. Local implications of almost global stability [Preprint] Publicado en Dynamical Systems, 2009, v. 24, no. 1, doi: 10.1080/14689360802474657https://hdl.handle.net/20.500.12008/38675We prove that for autonomous differential equations with the origin as a fixed point, and with at least one eigenvalue with negative real part, we have that the existence of a density function implies local asymptotical stability. We present examples of a system admitting a density function for which the origin is not locally asymptotically stable and an almost globally stable system for which no function is a density function. Keywords: nonlinear systems, asymptotical stability, density functions, almost global stabilitynbsp,Made available in DSpace on 2023-08-01T20:33:17Z (GMT). No. of bitstreams: 5 PM09.pdf: 172106 bytes, checksum: 9e00492a44039575c889eebdf83eda12 (MD5) license_text: 21936 bytes, checksum: 9833653f73f7853880c94a6fead477b1 (MD5) license_url: 49 bytes, checksum: 4afdbb8c545fd630ea7db775da747b2f (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) license.txt: 4194 bytes, checksum: 7f2e2c17ef6585de66da58d1bfa8b5e1 (MD5) Previous issue date: 2009enengLas obras depositadas en el Repositorio se rigen por la Ordenanza de los Derechos de la Propiedad Intelectual de la Universidad De La República. (Res. Nº 91 de C.D.C. de 8/III/1994 – D.O. 7/IV/1994) y por la Ordenanza del Repositorio Abierto de la Universidad de la República (Res. Nº 16 de C.D.C. de 07/10/2014)info:eu-repo/semantics/openAccessLicencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)Nonlinear systemsAsymptotical stabilityDensity functionsAlmost global stabilityLocal implications of almost global stabilityPreprintinfo:eu-repo/semantics/preprintinfo:eu-repo/semantics/submittedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaPotrie, RafaelMonzón, 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- Universidad de la Repúblicafalse |
| spellingShingle | Local implications of almost global stability Potrie, Rafael Nonlinear systems Asymptotical stability Density functions Almost global stability |
| status_str | submittedVersion |
| title | Local implications of almost global stability |
| title_full | Local implications of almost global stability |
| title_fullStr | Local implications of almost global stability |
| title_full_unstemmed | Local implications of almost global stability |
| title_short | Local implications of almost global stability |
| title_sort | Local implications of almost global stability |
| topic | Nonlinear systems Asymptotical stability Density functions Almost global stability |
| url | https://hdl.handle.net/20.500.12008/38675 |
