{"id":"https://openalex.org/W2784265887","doi":"https://doi.org/10.1109/cdc.2017.8263724","title":"Approximating periodic trajectories of contractive systems","display_name":"Approximating periodic trajectories of contractive systems","publication_year":2017,"publication_date":"2017-12-01","ids":{"openalex":"https://openalex.org/W2784265887","doi":"https://doi.org/10.1109/cdc.2017.8263724","mag":"2784265887"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2017.8263724","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2017.8263724","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 IEEE 56th Annual Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5074869481","display_name":"Michael Margaliot","orcid":"https://orcid.org/0000-0001-8319-8996"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Michael Margaliot","raw_affiliation_strings":["School of Electrical Engineering and the Sagol School of Neuroscience, Tel-Aviv University, Tel-Aviv, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering and the Sagol School of Neuroscience, Tel-Aviv University, Tel-Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010552433","display_name":"Samuel Coogan","orcid":"https://orcid.org/0000-0003-0495-1535"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Samuel Coogan","raw_affiliation_strings":["Department of Electrical Engineering, University of California, Los Angeles"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of California, Los Angeles","institution_ids":["https://openalex.org/I161318765"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"583","last_page":"588"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9997000098228455,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9997000098228455,"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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11125","display_name":"Petri Nets in System Modeling","score":0.9581999778747559,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.746496856212616},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6591806411743164},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6053332090377808},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5322332978248596},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.5280480980873108},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.49507537484169006},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4749988317489624},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.46243107318878174},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45662036538124084},{"id":"https://openalex.org/keywords/stability-theory","display_name":"Stability theory","score":0.43670180439949036},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2731502652168274},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22978746891021729},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1411409080028534},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.07277897000312805},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07077682018280029}],"concepts":[{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.746496856212616},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6591806411743164},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6053332090377808},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5322332978248596},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.5280480980873108},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.49507537484169006},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4749988317489624},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.46243107318878174},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45662036538124084},{"id":"https://openalex.org/C41949839","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theory","level":3,"score":0.43670180439949036},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2731502652168274},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22978746891021729},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1411409080028534},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.07277897000312805},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07077682018280029},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"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/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2017.8263724","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2017.8263724","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 IEEE 56th Annual Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W26528315","https://openalex.org/W55814457","https://openalex.org/W191357446","https://openalex.org/W1970592681","https://openalex.org/W1976515682","https://openalex.org/W1987185728","https://openalex.org/W1997741068","https://openalex.org/W1998042408","https://openalex.org/W2015464381","https://openalex.org/W2015745168","https://openalex.org/W2024171867","https://openalex.org/W2036216368","https://openalex.org/W2038750939","https://openalex.org/W2044062811","https://openalex.org/W2056706729","https://openalex.org/W2060612291","https://openalex.org/W2094935658","https://openalex.org/W2118430238","https://openalex.org/W2134889984","https://openalex.org/W2136351630","https://openalex.org/W2150495686","https://openalex.org/W2154278056","https://openalex.org/W2184636647","https://openalex.org/W2294343283","https://openalex.org/W2399827221","https://openalex.org/W2493555073","https://openalex.org/W2521919557","https://openalex.org/W2570513205","https://openalex.org/W2589221162","https://openalex.org/W2962871810","https://openalex.org/W2963680556"],"related_works":["https://openalex.org/W2592405099","https://openalex.org/W2938514635","https://openalex.org/W4360764540","https://openalex.org/W4231657010","https://openalex.org/W2041424614","https://openalex.org/W2012002054","https://openalex.org/W2007917622","https://openalex.org/W2783536463","https://openalex.org/W1994552539","https://openalex.org/W2888156545"],"abstract_inverted_index":{"We":[0,59,98,111],"consider":[1],"contractive":[2,96],"systems":[3,119],"whose":[4],"trajectories":[5],"evolve":[6],"on":[7,41,48,90],"a":[8,31,66,74],"compact":[9],"and":[10,45,55],"convex":[11],"state-space.":[12],"It":[13],"is":[14,25,51,88],"well-known":[15],"that":[16,87,100],"if":[17],"the":[18,23,28,70,91],"time-varying":[19],"vector":[20],"field":[21],"of":[22,73,95],"system":[24,29,76],"periodic":[26,36,43,67,71],"then":[27],"admits":[30],"unique":[32],"globally":[33],"asymptotically":[34],"stable":[35],"solution.":[37],"Obtaining":[38],"explicit":[39],"information":[40],"this":[42,104],"solution":[44],"its":[46],"dependence":[47],"various":[49],"parameters":[50],"important":[52],"both":[53],"theoretically":[54],"in":[56,101],"numerous":[57],"applications.":[58],"develop":[60],"an":[61,78,84],"approach":[62],"for":[63],"approximating":[64],"such":[65],"trajectory":[68,72],"using":[69,115],"simpler":[75],"(e.g.":[77],"LTI":[79],"system).":[80],"Our":[81],"approximation":[82],"includes":[83],"error":[85,105],"bound":[86,106],"based":[89],"input-to-state":[92],"stability":[93],"property":[94],"systems.":[97],"show":[99],"some":[102],"cases":[103],"can":[107],"be":[108],"computed":[109],"explicitly.":[110],"demonstrate":[112],"our":[113],"results":[114],"several":[116],"examples":[117],"from":[118],"biology.":[120]},"counts_by_year":[{"year":2018,"cited_by_count":3}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}