{"id":"https://openalex.org/W2993990461","doi":"https://doi.org/10.1109/tac.2019.2909815","title":"On Sufficient Conditions for Mixed Monotonicity","display_name":"On Sufficient Conditions for Mixed Monotonicity","publication_year":2019,"publication_date":"2019-12-01","ids":{"openalex":"https://openalex.org/W2993990461","doi":"https://doi.org/10.1109/tac.2019.2909815","mag":"2993990461"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2019.2909815","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2019.2909815","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/A5052314881","display_name":"Liren Yang","orcid":"https://orcid.org/0000-0002-7677-8543"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Liren Yang","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, USA","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040080749","display_name":"Oscar Mickelin","orcid":"https://orcid.org/0000-0003-0167-1992"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Oscar Mickelin","raw_affiliation_strings":["Department of Mathematics, Massachusetts Institute of Technology, Cambridge, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Massachusetts Institute of Technology, Cambridge, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054418471","display_name":"Necmiye \u00d6zay","orcid":"https://orcid.org/0000-0002-5552-4392"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Necmiye Ozay","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, USA","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5052314881"],"corresponding_institution_ids":["https://openalex.org/I27837315"],"apc_list":null,"apc_paid":null,"fwci":4.8232,"has_fulltext":false,"cited_by_count":47,"citation_normalized_percentile":{"value":0.95637545,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"64","issue":"12","first_page":"5080","last_page":"5085"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9994999766349792,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9994999766349792,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9987000226974487,"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/T11236","display_name":"Control Systems and Identification","score":0.9983000159263611,"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/monotonic-function","display_name":"Monotonic function","score":0.8890141844749451},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.8447543382644653},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5917252898216248},{"id":"https://openalex.org/keywords/abstraction","display_name":"Abstraction","score":0.5784577131271362},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.568087100982666},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5491290092468262},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.47662413120269775},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4615907669067383},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.43896815180778503},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.43507182598114014},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.41209617257118225},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.365821897983551},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.31902649998664856},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1130819320678711},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07940933108329773}],"concepts":[{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.8890141844749451},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.8447543382644653},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5917252898216248},{"id":"https://openalex.org/C124304363","wikidata":"https://www.wikidata.org/wiki/Q673661","display_name":"Abstraction","level":2,"score":0.5784577131271362},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.568087100982666},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5491290092468262},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.47662413120269775},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4615907669067383},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.43896815180778503},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.43507182598114014},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41209617257118225},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.365821897983551},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.31902649998664856},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1130819320678711},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07940933108329773},{"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2019.2909815","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2019.2909815","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"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.5600000023841858,"display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G111393173","display_name":null,"funder_award_id":"CNS-1446298","funder_id":"https://openalex.org/F4320307103","funder_display_name":"Ford Motor Company"},{"id":"https://openalex.org/G2749335301","display_name":null,"funder_award_id":"N66001-14-1-4045","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"},{"id":"https://openalex.org/G5968854864","display_name":null,"funder_award_id":"ECCS-1553873","funder_id":"https://openalex.org/F4320307103","funder_display_name":"Ford Motor Company"}],"funders":[{"id":"https://openalex.org/F4320307103","display_name":"Ford Motor Company","ror":"https://ror.org/00g2tkw06"},{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W183902185","https://openalex.org/W2048723778","https://openalex.org/W2062057326","https://openalex.org/W2065798383","https://openalex.org/W2079443759","https://openalex.org/W2120430892","https://openalex.org/W2147741970","https://openalex.org/W2594675090","https://openalex.org/W2594891385","https://openalex.org/W2603469395","https://openalex.org/W2735612372","https://openalex.org/W2791208186","https://openalex.org/W2949475222","https://openalex.org/W2964187244","https://openalex.org/W2964227708","https://openalex.org/W4250589301","https://openalex.org/W4285719527","https://openalex.org/W6734870313"],"related_works":["https://openalex.org/W1489292980","https://openalex.org/W2795079910","https://openalex.org/W2951610245","https://openalex.org/W1430963189","https://openalex.org/W1974262772","https://openalex.org/W2049901819","https://openalex.org/W3037410748","https://openalex.org/W2052430123","https://openalex.org/W1983437306","https://openalex.org/W4387778523"],"abstract_inverted_index":{"Mixed":[0],"monotone":[1,56,66],"systems":[2,9],"form":[3],"an":[4],"important":[5],"class":[6],"of":[7,37,54,105],"nonlinear":[8],"that":[10,89],"have":[11],"recently":[12],"received":[13],"attention":[14],"in":[15,25,40],"the":[16,26,48,79,82,102,106],"abstraction-based":[17],"control":[18,84],"design":[19],"area.":[20],"Slightly":[21],"different":[22,51],"definitions":[23,53],"exist":[24],"literature,":[27,85],"and":[28,58,86],"it":[29],"remains":[30],"a":[31,38,93],"challenge":[32],"to":[33],"verify":[34],"mixed":[35,55,65,90],"monotonicity":[36,91],"system":[39],"general.":[41],"In":[42],"this":[43],"paper,":[44],"we":[45],"first":[46],"clarify":[47],"relation":[49],"between":[50],"existing":[52,83],"systems,":[57],"then":[59],"give":[60],"two":[61],"sufficient":[62,73,108],"conditions":[63,74],"for":[64],"functions":[67],"defined":[68],"on":[69,101],"Euclidean":[70],"space.":[71],"These":[72],"are":[75,99],"more":[76],"general":[77],"than":[78],"ones":[80],"from":[81],"they":[87],"suggest":[88],"is":[92],"very":[94],"generic":[95],"property.":[96],"Some":[97],"discussions":[98],"provided":[100],"computational":[103],"usefulness":[104],"proposed":[107],"conditions.":[109]},"counts_by_year":[{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}