{"id":"https://openalex.org/W2743365471","doi":"https://doi.org/10.1109/tac.2017.2735194","title":"Nonconservative Discrete-Time ISS Small-Gain Conditions for Closed Sets","display_name":"Nonconservative Discrete-Time ISS Small-Gain Conditions for Closed Sets","publication_year":2017,"publication_date":"2017-08-02","ids":{"openalex":"https://openalex.org/W2743365471","doi":"https://doi.org/10.1109/tac.2017.2735194","mag":"2743365471"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2017.2735194","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2017.2735194","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-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/A5032077951","display_name":"Navid Noroozi","orcid":"https://orcid.org/0000-0002-9399-9938"},"institutions":[{"id":"https://openalex.org/I186354981","display_name":"University of Passau","ror":"https://ror.org/05ydjnb78","country_code":"DE","type":"education","lineage":["https://openalex.org/I186354981"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Navid Noroozi","raw_affiliation_strings":["Faculty of Computer Science and Mathematics, University of Passau, Passau, Germany"],"affiliations":[{"raw_affiliation_string":"Faculty of Computer Science and Mathematics, University of Passau, Passau, Germany","institution_ids":["https://openalex.org/I186354981"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090886281","display_name":"Roman Geiselhart","orcid":"https://orcid.org/0000-0001-6382-8305"},"institutions":[{"id":"https://openalex.org/I196349391","display_name":"Universit\u00e4t Ulm","ror":"https://ror.org/032000t02","country_code":"DE","type":"education","lineage":["https://openalex.org/I196349391"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Roman Geiselhart","raw_affiliation_strings":["Institute of Measurement, Control and Microtechnology, University of Ulm, Ulm, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Measurement, Control and Microtechnology, University of Ulm, Ulm, Germany","institution_ids":["https://openalex.org/I196349391"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054568856","display_name":"Lars Gr\u00fcne","orcid":"https://orcid.org/0000-0002-9331-4097"},"institutions":[{"id":"https://openalex.org/I54009628","display_name":"University of Bayreuth","ror":"https://ror.org/0234wmv40","country_code":"DE","type":"education","lineage":["https://openalex.org/I54009628"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Lars Grune","raw_affiliation_strings":["Mathematical Institute, University of Bayreuth, Bayreuth, Germany"],"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Bayreuth, Bayreuth, Germany","institution_ids":["https://openalex.org/I54009628"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040557933","display_name":"Bj\u00f6rn S. R\u00fcffer","orcid":"https://orcid.org/0000-0001-8180-9773"},"institutions":[{"id":"https://openalex.org/I78757542","display_name":"University of Newcastle Australia","ror":"https://ror.org/00eae9z71","country_code":"AU","type":"education","lineage":["https://openalex.org/I78757542"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Bjorn S. Ruffer","raw_affiliation_strings":["Faculty of Science, University of Newcastle, Callaghan, NSW, Australia"],"affiliations":[{"raw_affiliation_string":"Faculty of Science, University of Newcastle, Callaghan, NSW, Australia","institution_ids":["https://openalex.org/I78757542"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036100755","display_name":"Fabian Wirth","orcid":"https://orcid.org/0000-0002-2123-3714"},"institutions":[{"id":"https://openalex.org/I186354981","display_name":"University of Passau","ror":"https://ror.org/05ydjnb78","country_code":"DE","type":"education","lineage":["https://openalex.org/I186354981"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Fabian R. Wirth","raw_affiliation_strings":["Faculty of Computer Science and Mathematics, University of Passau, Passau, Germany"],"affiliations":[{"raw_affiliation_string":"Faculty of Computer Science and Mathematics, University of Passau, Passau, Germany","institution_ids":["https://openalex.org/I186354981"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5032077951"],"corresponding_institution_ids":["https://openalex.org/I186354981"],"apc_list":null,"apc_paid":null,"fwci":3.822,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.93624618,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"63","issue":"5","first_page":"1231","last_page":"1242"},"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":0.9995999932289124,"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":0.9995999932289124,"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9976000189781189,"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"}},{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9955999851226807,"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/control-theory","display_name":"Control theory (sociology)","score":0.684424877166748},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.6047242283821106},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5840267539024353},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5803715586662292},{"id":"https://openalex.org/keywords/synchronization","display_name":"Synchronization (alternating current)","score":0.5571552515029907},{"id":"https://openalex.org/keywords/unification","display_name":"Unification","score":0.5111790299415588},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4542035758495331},{"id":"https://openalex.org/keywords/small-gain-theorem","display_name":"Small-gain theorem","score":0.41537144780158997},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3728329539299011},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.21756485104560852},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.1294126808643341},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.11146369576454163},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0837198793888092},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07110944390296936}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.684424877166748},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6047242283821106},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5840267539024353},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5803715586662292},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.5571552515029907},{"id":"https://openalex.org/C96146094","wikidata":"https://www.wikidata.org/wiki/Q609057","display_name":"Unification","level":2,"score":0.5111790299415588},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4542035758495331},{"id":"https://openalex.org/C27385263","wikidata":"https://www.wikidata.org/wiki/Q4165677","display_name":"Small-gain theorem","level":3,"score":0.41537144780158997},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3728329539299011},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.21756485104560852},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.1294126808643341},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.11146369576454163},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0837198793888092},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07110944390296936},{"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/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tac.2017.2735194","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2017.2735194","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:eref.uni-bayreuth.de:39076","is_oa":false,"landing_page_url":"https://eref.uni-bayreuth.de/39076/","pdf_url":null,"source":{"id":"https://openalex.org/S4377196442","display_name":"ERef Bayreuth (University of Bayreuth)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I54009628","host_organization_name":"University of Bayreuth","host_organization_lineage":["https://openalex.org/I54009628"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Artikel in einer Zeitschrift"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320308269","display_name":"Alexander von Humboldt-Stiftung","ror":"https://ror.org/012kf4317"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W617909835","https://openalex.org/W1491672380","https://openalex.org/W1532162288","https://openalex.org/W1565805093","https://openalex.org/W1979295221","https://openalex.org/W1985813210","https://openalex.org/W1994003949","https://openalex.org/W1995313864","https://openalex.org/W2003504842","https://openalex.org/W2005390836","https://openalex.org/W2009668633","https://openalex.org/W2010145070","https://openalex.org/W2017493230","https://openalex.org/W2020588182","https://openalex.org/W2028462202","https://openalex.org/W2038137192","https://openalex.org/W2052089350","https://openalex.org/W2058731737","https://openalex.org/W2059527961","https://openalex.org/W2060161410","https://openalex.org/W2083195399","https://openalex.org/W2087219491","https://openalex.org/W2098989671","https://openalex.org/W2107396783","https://openalex.org/W2109997451","https://openalex.org/W2117079884","https://openalex.org/W2134078068","https://openalex.org/W2135653743","https://openalex.org/W2159479095","https://openalex.org/W2162053828","https://openalex.org/W2163718740","https://openalex.org/W2165626406","https://openalex.org/W2203684142","https://openalex.org/W2291587244","https://openalex.org/W2569328136","https://openalex.org/W2571200063","https://openalex.org/W2602502146","https://openalex.org/W2733464043","https://openalex.org/W2963176150","https://openalex.org/W2963785007","https://openalex.org/W2963923230","https://openalex.org/W3101604534","https://openalex.org/W4301465697","https://openalex.org/W6687744256","https://openalex.org/W6720189883","https://openalex.org/W6731422777"],"related_works":["https://openalex.org/W2620928602","https://openalex.org/W2098989671","https://openalex.org/W2099438021","https://openalex.org/W2571307628","https://openalex.org/W2038920950","https://openalex.org/W3138295754","https://openalex.org/W4376456722","https://openalex.org/W2133447038","https://openalex.org/W1990502710","https://openalex.org/W2159479095"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3,6,13,47,67],"unification":[4],"and":[5,29,87],"generalization":[7],"of":[8,16,50,66,69,73,80],"the":[9,60],"small-gain":[10,18,24,61],"theory":[11],"subsuming":[12],"wide":[14],"range":[15],"existing":[17],"theorems.":[19],"In":[20],"particular,":[21],"we":[22,44,58],"introduce":[23],"conditions":[25,62],"that":[26],"are":[27,90],"necessary":[28],"sufficient":[30],"to":[31,38,63,76],"ensure":[32],"input-to-state":[33],"stability":[34],"(ISS)":[35],"with":[36],"respect":[37],"closed":[39],"sets.":[40],"Toward":[41],"this":[42],"end,":[43],"first":[45],"develop":[46],"Lyapunov":[48,55],"characterization":[49],"\u03c9ISS":[51,54,65],"via":[52],"finite-step":[53],"functions.":[56],"Then,":[57],"provide":[59],"guarantee":[64],"network":[68],"systems.":[70],"Finally,":[71],"applications":[72],"our":[74],"results":[75],"partial":[77],"ISS,":[78],"ISS":[79],"time-varying":[81],"systems,":[82],"synchronization":[83],"problems,":[84],"incremental":[85],"stability,":[86],"distributed":[88],"observers":[89],"given.":[91]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
