{"id":"https://openalex.org/W2150936942","doi":"https://doi.org/10.1109/cdc.2007.4434221","title":"Zero patterns and dominant modes of the state evolutions of autonomous continuous-time positive systems","display_name":"Zero patterns and dominant modes of the state evolutions of autonomous continuous-time positive systems","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2150936942","doi":"https://doi.org/10.1109/cdc.2007.4434221","mag":"2150936942"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2007.4434221","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2007.4434221","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 46th IEEE Conference on Decision and Control","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018527161","display_name":"Paolo Santesso","orcid":null},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Paolo Santesso","raw_affiliation_strings":["Dipartimento diIngegneria dellInformazione, Universit\u00e0 di Padova, Padova, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento diIngegneria dellInformazione, Universit\u00e0 di Padova, Padova, Italy","institution_ids":["https://openalex.org/I138689650"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064493313","display_name":"Maria Elena Valcher","orcid":"https://orcid.org/0000-0002-7595-3688"},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Maria Elena Valcher","raw_affiliation_strings":["Dipartimento diIngegneria dellInformazione, Universit\u00e0 di Padova, Padova, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento diIngegneria dellInformazione, Universit\u00e0 di Padova, Padova, Italy","institution_ids":["https://openalex.org/I138689650"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16686063,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"38","issue":null,"first_page":"482","last_page":"487"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.7257226705551147},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5984423756599426},{"id":"https://openalex.org/keywords/zero-mode","display_name":"Zero mode","score":0.5892148613929749},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5663345456123352},{"id":"https://openalex.org/keywords/mode","display_name":"Mode (computer interface)","score":0.5449354648590088},{"id":"https://openalex.org/keywords/exponential-growth","display_name":"Exponential growth","score":0.5354196429252625},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5208069086074829},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5014009475708008},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.41909921169281006},{"id":"https://openalex.org/keywords/matrix-exponential","display_name":"Matrix exponential","score":0.4190191328525543},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.41503196954727173},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.38495302200317383},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.34420639276504517},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27958714962005615},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2716323137283325},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.21899104118347168},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.20393815636634827},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12637373805046082},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11094650626182556},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.08276501297950745},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.07720592617988586}],"concepts":[{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.7257226705551147},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5984423756599426},{"id":"https://openalex.org/C2780658932","wikidata":"https://www.wikidata.org/wiki/Q8069598","display_name":"Zero mode","level":2,"score":0.5892148613929749},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5663345456123352},{"id":"https://openalex.org/C48677424","wikidata":"https://www.wikidata.org/wiki/Q6888088","display_name":"Mode (computer interface)","level":2,"score":0.5449354648590088},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.5354196429252625},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5208069086074829},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5014009475708008},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.41909921169281006},{"id":"https://openalex.org/C195906000","wikidata":"https://www.wikidata.org/wiki/Q1191722","display_name":"Matrix exponential","level":3,"score":0.4190191328525543},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.41503196954727173},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.38495302200317383},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.34420639276504517},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27958714962005615},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2716323137283325},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21899104118347168},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.20393815636634827},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12637373805046082},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11094650626182556},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.08276501297950745},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.07720592617988586},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/cdc.2007.4434221","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2007.4434221","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 46th IEEE Conference on Decision and Control","raw_type":"proceedings-article"},{"id":"pmh:oai:www.research.unipd.it:11577/1781075","is_oa":false,"landing_page_url":"http://hdl.handle.net/11577/1781075","pdf_url":null,"source":{"id":"https://openalex.org/S4377196283","display_name":"Research Padua  Archive (University of Padua)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I138689650","host_organization_name":"University of Padua","host_organization_lineage":["https://openalex.org/I138689650"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1500921805","https://openalex.org/W1529274881","https://openalex.org/W1534430411","https://openalex.org/W1568175246","https://openalex.org/W1983868185","https://openalex.org/W1994635232","https://openalex.org/W1994823943","https://openalex.org/W1995262249","https://openalex.org/W1996551653","https://openalex.org/W2023010641","https://openalex.org/W2036521469","https://openalex.org/W2065043015","https://openalex.org/W2069221621","https://openalex.org/W2104017916","https://openalex.org/W2104426166","https://openalex.org/W2132210216","https://openalex.org/W2137665908","https://openalex.org/W2143461633","https://openalex.org/W2150594195","https://openalex.org/W2156502660","https://openalex.org/W2171978643","https://openalex.org/W2275045947","https://openalex.org/W2277485965","https://openalex.org/W2481886882","https://openalex.org/W4235143360","https://openalex.org/W4299798129","https://openalex.org/W6694777769"],"related_works":["https://openalex.org/W3099959778","https://openalex.org/W2950706997","https://openalex.org/W2075592594","https://openalex.org/W4394883359","https://openalex.org/W4238625510","https://openalex.org/W2055480472","https://openalex.org/W1602624896","https://openalex.org/W4317660424","https://openalex.org/W1982776613","https://openalex.org/W1519862060"],"abstract_inverted_index":{"In":[0],"this":[1,23],"paper,":[2],"the":[3,8,12,29,38,52,61,65,73,79,88,92],"zero":[4,74,89],"pattern":[5,75,90],"properties":[6],"and":[7,37],"asymptotic":[9],"evolution":[10],"of":[11,14,31,40,48,55,64,82,91],"trajectories":[13],"an":[15],"autonomous":[16],"continuous-time":[17],"positive":[18],"system":[19],"are":[20],"investigated.":[21],"To":[22],"end,":[24],"a":[25,32,71],"normal":[26,62],"form":[27,63],"for":[28],"exponential":[30,66],"Metzler":[33],"matrix":[34,67],"is":[35,43,68],"provided,":[36],"concept":[39],"\"echelon":[41],"basis\"":[42],"introduced.":[44],"By":[45],"making":[46],"use":[47],"these":[49],"two":[50],"ingredients,":[51],"dominant":[53,80],"mode":[54,81],"each":[56],"single":[57],"block":[58],"appearing":[59],"in":[60],"determined.":[69],"As":[70],"result,":[72],"as":[76,78],"well":[77],"every":[83],"state":[84],"evolution,":[85],"depending":[86],"on":[87],"initial":[93],"state,":[94],"can":[95],"be":[96],"easily":[97],"inferred.":[98]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}