Loading…
Computation and stability of limit cycles in hybrid systems
In this note, a practical way to compute limit cycles in context of hybrid systems is investigated. As in many hybrid applications the steady state is depicted by a limit cycle, control design and stability analysis of such hybrid systems require the knowledge of this periodic motion. Analytical exp...
Saved in:
Published in: | Nonlinear analysis 2006-01, Vol.64 (2), p.352-367 |
---|---|
Main Authors: | , , |
Format: | Article |
Language: | English |
Subjects: | |
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-c401t-7d3b9c55bdf24f19903f230e6ab17b2d72db01d1a62fa66e22eee4bc7d92c6823 |
---|---|
cites | cdi_FETCH-LOGICAL-c401t-7d3b9c55bdf24f19903f230e6ab17b2d72db01d1a62fa66e22eee4bc7d92c6823 |
container_end_page | 367 |
container_issue | 2 |
container_start_page | 352 |
container_title | Nonlinear analysis |
container_volume | 64 |
creator | Flieller, D. Riedinger, P. Louis, J.P. |
description | In this note, a practical way to compute limit cycles in context of hybrid systems is investigated. As in many hybrid applications the steady state is depicted by a limit cycle, control design and stability analysis of such hybrid systems require the knowledge of this periodic motion. Analytical expression of this cycle is generally an impossible task due to the complexity of the dynamic. A fast algorithm is proposed and used to determine these cycles in the case where the switching sequence is known.
The proposed method is based on the rule played by the switching times in the sensitivity functions.
The stability of the cycle is also deduced at the end of the run thanks to the computation of the Jacobian matrix of the linearized sampled time systems.
This work can be used as a starting point for sensitivity analysis, measurement of attraction area and control design. |
doi_str_mv | 10.1016/j.na.2005.06.054 |
format | article |
fullrecord | <record><control><sourceid>proquest_hal_p</sourceid><recordid>TN_cdi_hal_primary_oai_HAL_hal_00119807v1</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0362546X05007030</els_id><sourcerecordid>29152203</sourcerecordid><originalsourceid>FETCH-LOGICAL-c401t-7d3b9c55bdf24f19903f230e6ab17b2d72db01d1a62fa66e22eee4bc7d92c6823</originalsourceid><addsrcrecordid>eNp1kM9LwzAYhoMoOKd3jz0JHlq_JE266mkMdcLAi4K3kCZfWUZ_zCQb9L-3o-LN0wcfz_PC-xJySyGjQOXDLut0xgBEBjIDkZ-RGV0UPBWMinMyAy5ZKnL5dUmuQtgBAC24nJGnVd_uD1FH13eJ7mwSoq5c4-KQ9HXSuNbFxAymwZC4LtkOlXcjM4SIbbgmF7VuAt783jn5fHn-WK3Tzfvr22q5SU0ONKaF5VVphKhszfKaliXwmnFAqStaVMwWzFZALdWS1VpKZAwR88oUtmRGLhifk_spd6sbtfeu1X5QvXZqvdyo028sQ8sFFEc6sncTu_f99wFDVK0LBptGd9gfgmIlFYwBH0GYQOP7EDzWf8kU1GlRtVOdVqdFFUg1Ljoqj5OCY9mjQ6-CcdgZtM6jicr27n_5Byp6fMw</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>29152203</pqid></control><display><type>article</type><title>Computation and stability of limit cycles in hybrid systems</title><source>ScienceDirect Freedom Collection</source><source>Backfile Package - Mathematics (Legacy) [YMT]</source><creator>Flieller, D. ; Riedinger, P. ; Louis, J.P.</creator><creatorcontrib>Flieller, D. ; Riedinger, P. ; Louis, J.P.</creatorcontrib><description>In this note, a practical way to compute limit cycles in context of hybrid systems is investigated. As in many hybrid applications the steady state is depicted by a limit cycle, control design and stability analysis of such hybrid systems require the knowledge of this periodic motion. Analytical expression of this cycle is generally an impossible task due to the complexity of the dynamic. A fast algorithm is proposed and used to determine these cycles in the case where the switching sequence is known.
The proposed method is based on the rule played by the switching times in the sensitivity functions.
The stability of the cycle is also deduced at the end of the run thanks to the computation of the Jacobian matrix of the linearized sampled time systems.
This work can be used as a starting point for sensitivity analysis, measurement of attraction area and control design.</description><identifier>ISSN: 0362-546X</identifier><identifier>EISSN: 1873-5215</identifier><identifier>DOI: 10.1016/j.na.2005.06.054</identifier><language>eng</language><publisher>Elsevier Ltd</publisher><subject>Automatic ; Condensed Matter ; Electric power ; Electromagnetism ; Engineering Sciences ; Hybrid systems ; Limit cycles ; Physics ; Power converters ; Sensitivity functions ; Stability ; Superconductivity</subject><ispartof>Nonlinear analysis, 2006-01, Vol.64 (2), p.352-367</ispartof><rights>2005</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c401t-7d3b9c55bdf24f19903f230e6ab17b2d72db01d1a62fa66e22eee4bc7d92c6823</citedby><cites>FETCH-LOGICAL-c401t-7d3b9c55bdf24f19903f230e6ab17b2d72db01d1a62fa66e22eee4bc7d92c6823</cites><orcidid>0000-0002-8221-4736</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0362546X05007030$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>230,314,776,780,881,3551,27901,27902,45978</link.rule.ids><backlink>$$Uhttps://hal.science/hal-00119807$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Flieller, D.</creatorcontrib><creatorcontrib>Riedinger, P.</creatorcontrib><creatorcontrib>Louis, J.P.</creatorcontrib><title>Computation and stability of limit cycles in hybrid systems</title><title>Nonlinear analysis</title><description>In this note, a practical way to compute limit cycles in context of hybrid systems is investigated. As in many hybrid applications the steady state is depicted by a limit cycle, control design and stability analysis of such hybrid systems require the knowledge of this periodic motion. Analytical expression of this cycle is generally an impossible task due to the complexity of the dynamic. A fast algorithm is proposed and used to determine these cycles in the case where the switching sequence is known.
The proposed method is based on the rule played by the switching times in the sensitivity functions.
The stability of the cycle is also deduced at the end of the run thanks to the computation of the Jacobian matrix of the linearized sampled time systems.
This work can be used as a starting point for sensitivity analysis, measurement of attraction area and control design.</description><subject>Automatic</subject><subject>Condensed Matter</subject><subject>Electric power</subject><subject>Electromagnetism</subject><subject>Engineering Sciences</subject><subject>Hybrid systems</subject><subject>Limit cycles</subject><subject>Physics</subject><subject>Power converters</subject><subject>Sensitivity functions</subject><subject>Stability</subject><subject>Superconductivity</subject><issn>0362-546X</issn><issn>1873-5215</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2006</creationdate><recordtype>article</recordtype><recordid>eNp1kM9LwzAYhoMoOKd3jz0JHlq_JE266mkMdcLAi4K3kCZfWUZ_zCQb9L-3o-LN0wcfz_PC-xJySyGjQOXDLut0xgBEBjIDkZ-RGV0UPBWMinMyAy5ZKnL5dUmuQtgBAC24nJGnVd_uD1FH13eJ7mwSoq5c4-KQ9HXSuNbFxAymwZC4LtkOlXcjM4SIbbgmF7VuAt783jn5fHn-WK3Tzfvr22q5SU0ONKaF5VVphKhszfKaliXwmnFAqStaVMwWzFZALdWS1VpKZAwR88oUtmRGLhifk_spd6sbtfeu1X5QvXZqvdyo028sQ8sFFEc6sncTu_f99wFDVK0LBptGd9gfgmIlFYwBH0GYQOP7EDzWf8kU1GlRtVOdVqdFFUg1Ljoqj5OCY9mjQ6-CcdgZtM6jicr27n_5Byp6fMw</recordid><startdate>20060101</startdate><enddate>20060101</enddate><creator>Flieller, D.</creator><creator>Riedinger, P.</creator><creator>Louis, J.P.</creator><general>Elsevier Ltd</general><general>Elsevier</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>1XC</scope><scope>VOOES</scope><orcidid>https://orcid.org/0000-0002-8221-4736</orcidid></search><sort><creationdate>20060101</creationdate><title>Computation and stability of limit cycles in hybrid systems</title><author>Flieller, D. ; Riedinger, P. ; Louis, J.P.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c401t-7d3b9c55bdf24f19903f230e6ab17b2d72db01d1a62fa66e22eee4bc7d92c6823</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2006</creationdate><topic>Automatic</topic><topic>Condensed Matter</topic><topic>Electric power</topic><topic>Electromagnetism</topic><topic>Engineering Sciences</topic><topic>Hybrid systems</topic><topic>Limit cycles</topic><topic>Physics</topic><topic>Power converters</topic><topic>Sensitivity functions</topic><topic>Stability</topic><topic>Superconductivity</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Flieller, D.</creatorcontrib><creatorcontrib>Riedinger, P.</creatorcontrib><creatorcontrib>Louis, J.P.</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts – Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>Nonlinear analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Flieller, D.</au><au>Riedinger, P.</au><au>Louis, J.P.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Computation and stability of limit cycles in hybrid systems</atitle><jtitle>Nonlinear analysis</jtitle><date>2006-01-01</date><risdate>2006</risdate><volume>64</volume><issue>2</issue><spage>352</spage><epage>367</epage><pages>352-367</pages><issn>0362-546X</issn><eissn>1873-5215</eissn><abstract>In this note, a practical way to compute limit cycles in context of hybrid systems is investigated. As in many hybrid applications the steady state is depicted by a limit cycle, control design and stability analysis of such hybrid systems require the knowledge of this periodic motion. Analytical expression of this cycle is generally an impossible task due to the complexity of the dynamic. A fast algorithm is proposed and used to determine these cycles in the case where the switching sequence is known.
The proposed method is based on the rule played by the switching times in the sensitivity functions.
The stability of the cycle is also deduced at the end of the run thanks to the computation of the Jacobian matrix of the linearized sampled time systems.
This work can be used as a starting point for sensitivity analysis, measurement of attraction area and control design.</abstract><pub>Elsevier Ltd</pub><doi>10.1016/j.na.2005.06.054</doi><tpages>16</tpages><orcidid>https://orcid.org/0000-0002-8221-4736</orcidid><oa>free_for_read</oa></addata></record> |
fulltext | fulltext |
identifier | ISSN: 0362-546X |
ispartof | Nonlinear analysis, 2006-01, Vol.64 (2), p.352-367 |
issn | 0362-546X 1873-5215 |
language | eng |
recordid | cdi_hal_primary_oai_HAL_hal_00119807v1 |
source | ScienceDirect Freedom Collection; Backfile Package - Mathematics (Legacy) [YMT] |
subjects | Automatic Condensed Matter Electric power Electromagnetism Engineering Sciences Hybrid systems Limit cycles Physics Power converters Sensitivity functions Stability Superconductivity |
title | Computation and stability of limit cycles in hybrid systems |
url | http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-13T21%3A00%3A11IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_hal_p&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Computation%20and%20stability%20of%20limit%20cycles%20in%20hybrid%20systems&rft.jtitle=Nonlinear%20analysis&rft.au=Flieller,%20D.&rft.date=2006-01-01&rft.volume=64&rft.issue=2&rft.spage=352&rft.epage=367&rft.pages=352-367&rft.issn=0362-546X&rft.eissn=1873-5215&rft_id=info:doi/10.1016/j.na.2005.06.054&rft_dat=%3Cproquest_hal_p%3E29152203%3C/proquest_hal_p%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c401t-7d3b9c55bdf24f19903f230e6ab17b2d72db01d1a62fa66e22eee4bc7d92c6823%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=29152203&rft_id=info:pmid/&rfr_iscdi=true |