{"id":"https://openalex.org/W1995972356","doi":"https://doi.org/10.1137/s0363012903421200","title":"Graph Topologies, Gap Metrics, and Robust Stability for Nonlinear Systems","display_name":"Graph Topologies, Gap Metrics, and Robust Stability for Nonlinear Systems","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W1995972356","doi":"https://doi.org/10.1137/s0363012903421200","mag":"1995972356"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012903421200","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://eprints.soton.ac.uk/260187/1/siam03-10-04.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060932351","display_name":"W. Bian","orcid":"https://orcid.org/0009-0004-4063-1541"},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"W. Bian","raw_affiliation_strings":["Department of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, United Kingdom"],"affiliations":[{"raw_affiliation_string":"Department of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, United Kingdom","institution_ids":["https://openalex.org/I43439940"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038299372","display_name":"Martyn A. French","orcid":"https://orcid.org/0000-0002-4644-1982"},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"M. French","raw_affiliation_strings":["Department of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, United Kingdom"],"affiliations":[{"raw_affiliation_string":"Department of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, United Kingdom","institution_ids":["https://openalex.org/I43439940"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.162,"has_fulltext":true,"fulltext_origin":"pdf","cited_by_count":21,"citation_normalized_percentile":{"value":0.951228,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":87,"max":88},"biblio":{"volume":"44","issue":"2","first_page":"418","last_page":"443"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9989,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9989,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9983,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9962,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algebraic-connectivity","display_name":"Algebraic connectivity","score":0.44175932}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.80750954},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.67029136},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.52179575},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.44878885},{"id":"https://openalex.org/C7948225","wikidata":"https://www.wikidata.org/wiki/Q4723998","display_name":"Algebraic connectivity","level":4,"score":0.44175932},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4236776},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.32382768},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.31915742},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.27320215},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11012733},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012903421200","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://eprints.soton.ac.uk/260187/1/siam03-10-04.pdf","pdf_url":"https://eprints.soton.ac.uk/260187/1/siam03-10-04.pdf","source":{"id":"https://openalex.org/S4306401020","display_name":"ePrints Soton (University of Southampton)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":["University of Southampton"],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false},{"is_oa":true,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.572.1902","pdf_url":"http://eprints.soton.ac.uk/260187/1/siam03-10-04.pdf","source":{"id":"https://openalex.org/S4306400349","display_name":"CiteSeer X (The Pennsylvania State University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130769515","host_organization_name":"Pennsylvania State University","host_organization_lineage":["https://openalex.org/I130769515"],"host_organization_lineage_names":["Pennsylvania State University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://eprints.soton.ac.uk/260187/1/siam03-10-04.pdf","pdf_url":"https://eprints.soton.ac.uk/260187/1/siam03-10-04.pdf","source":{"id":"https://openalex.org/S4306401020","display_name":"ePrints Soton (University of Southampton)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":["University of Southampton"],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":23,"referenced_works":["https://openalex.org/W1489337560","https://openalex.org/W1887431197","https://openalex.org/W1971420010","https://openalex.org/W1983307430","https://openalex.org/W2017493230","https://openalex.org/W2023592020","https://openalex.org/W2030765412","https://openalex.org/W2038987621","https://openalex.org/W2098918927","https://openalex.org/W2106901410","https://openalex.org/W2121143119","https://openalex.org/W2121337039","https://openalex.org/W2127768514","https://openalex.org/W2166287780","https://openalex.org/W2169106716","https://openalex.org/W2177200371","https://openalex.org/W2177830233","https://openalex.org/W2179595285","https://openalex.org/W2484694144","https://openalex.org/W3023236793","https://openalex.org/W4214690803","https://openalex.org/W4285719527","https://openalex.org/W597526370"],"related_works":["https://openalex.org/W629610381","https://openalex.org/W4293490326","https://openalex.org/W2966981489","https://openalex.org/W2949145992","https://openalex.org/W2362020254","https://openalex.org/W2148597446","https://openalex.org/W2138547065","https://openalex.org/W2064571435","https://openalex.org/W2050710833","https://openalex.org/W1901677444"],"abstract_inverted_index":{"Graph":[0],"topologies":[1,36,56],"for":[2],"nonlinear":[3,43],"operators":[4],"which":[5],"admit":[6],"coprime":[7],"factorizations":[8],"are":[9,27,37,57,63],"defined":[10,29],"w.r.t.":[11,65],"a":[12,19,73],"gain":[13],"function":[14],"notion":[15],"of":[16,45,72],"stability":[17],"in":[18],"general":[20],"normed":[21],"signal":[22],"space":[23],"setting.":[24],"Several":[25],"metrics":[26],"also":[28],"and":[30,48,53],"their":[31],"relationship":[32],"to":[33],"the":[34,46,54,66,70,77],"graph":[35,49,55,67],"examined.":[38],"In":[39],"particular,":[40],"relationships":[41],"between":[42],"generalizations":[44],"gap":[47],"metrics,":[50],"Georgiou-type":[51],"formulae,":[52],"established.":[58],"Closed":[59],"loop":[60],"robustness":[61],"results":[62],"given":[64],"topology,":[68],"where":[69],"role":[71],"coercivity":[74],"condition":[75],"on":[76],"nominal":[78],"plant":[79],"is":[80],"emphasized.":[81]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W1995972356","counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2024-12-13T17:44:40.187015","created_date":"2016-06-24"}