{"id":"https://openalex.org/W2289290840","doi":"https://doi.org/10.1109/cdc.2015.7403363","title":"Optimization problems arising in stability analysis of discrete time nonlinear systems","display_name":"Optimization problems arising in stability analysis of discrete time nonlinear systems","publication_year":2015,"publication_date":"2015-12-01","ids":{"openalex":"https://openalex.org/W2289290840","doi":"https://doi.org/10.1109/cdc.2015.7403363","mag":"2289290840"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2015.7403363","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2015.7403363","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 54th IEEE Conference on Decision and Control (CDC)","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/A5038576809","display_name":"Nikita Barabanov","orcid":"https://orcid.org/0000-0003-2131-1572"},"institutions":[{"id":"https://openalex.org/I57328836","display_name":"North Dakota State University","ror":"https://ror.org/05h1bnb22","country_code":"US","type":"education","lineage":["https://openalex.org/I57328836"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nikita Barabanov","raw_affiliation_strings":["North Dakota State University, Fargo, ND, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"North Dakota State University, Fargo, ND, USA","institution_ids":["https://openalex.org/I57328836"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065785669","display_name":"Jayant Singh","orcid":"https://orcid.org/0000-0001-7205-2713"},"institutions":[{"id":"https://openalex.org/I57328836","display_name":"North Dakota State University","ror":"https://ror.org/05h1bnb22","country_code":"US","type":"education","lineage":["https://openalex.org/I57328836"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jayant Singh","raw_affiliation_strings":["North Dakota State University, Fargo, ND, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"North Dakota State University, Fargo, ND, USA","institution_ids":["https://openalex.org/I57328836"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I57328836"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.17089105,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":null,"first_page":"7250","last_page":"7255"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9991000294685364,"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"}},"topics":[{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9991000294685364,"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":0.9980000257492065,"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/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9970999956130981,"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/hyperplane","display_name":"Hyperplane","score":0.8058561086654663},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6654723286628723},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5970621705055237},{"id":"https://openalex.org/keywords/transfer-function","display_name":"Transfer function","score":0.5578389167785645},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5455760955810547},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5381589531898499},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5348156094551086},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.47862711548805237},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.47247761487960815},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.46988537907600403},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4683277904987335},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.4491366147994995},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.44715946912765503},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4333382844924927},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21775603294372559},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.136473149061203},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09789848327636719},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08394411206245422}],"concepts":[{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.8058561086654663},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6654723286628723},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5970621705055237},{"id":"https://openalex.org/C81299745","wikidata":"https://www.wikidata.org/wiki/Q334269","display_name":"Transfer function","level":2,"score":0.5578389167785645},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5455760955810547},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5381589531898499},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5348156094551086},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.47862711548805237},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.47247761487960815},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.46988537907600403},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4683277904987335},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.4491366147994995},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.44715946912765503},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4333382844924927},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21775603294372559},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.136473149061203},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09789848327636719},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08394411206245422},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2015.7403363","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2015.7403363","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 54th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1978127745","https://openalex.org/W1985779496","https://openalex.org/W2071464928","https://openalex.org/W2120472140","https://openalex.org/W2155176997","https://openalex.org/W2158773148"],"related_works":["https://openalex.org/W2369655046","https://openalex.org/W2019467317","https://openalex.org/W1585519779","https://openalex.org/W1965515989","https://openalex.org/W2088737283","https://openalex.org/W1999587863","https://openalex.org/W1929902734","https://openalex.org/W3104474499","https://openalex.org/W4376167435","https://openalex.org/W1965992231"],"abstract_inverted_index":{"We":[0,46],"consider":[1],"a":[2,53,84],"nonconvex":[3,32],"optimization":[4],"problem":[5],"arising":[6],"in":[7],"the":[8,25,73,90,93],"theory":[9],"of":[10,14,40,52,55,58,63,75,77,80,92],"global":[11],"asymptotic":[12],"stability":[13],"discrete":[15],"time":[16],"recurrent":[17],"neural":[18],"networks.":[19],"Under":[20],"certain":[21],"weak":[22],"conditions":[23,49],"on":[24],"transfer":[26,71],"functions":[27,60,72],"we":[28],"proved":[29],"that":[30,68],"corresponding":[31],"cost":[33,59,81],"function":[34,82],"has":[35],"at":[36],"most":[37],"one":[38],"point":[39,54],"local":[41,56,78],"maximum":[42,57,79],"over":[43,61,83],"every":[44],"hyperplane.":[45],"derived":[47],"sufficient":[48],"for":[50,69],"existence":[51],"planes":[62],"less":[64],"dimensions,":[65],"and":[66],"show":[67],"standard":[70],"number":[74],"points":[76],"plane":[85],"may":[86],"be":[87],"bigger":[88],"than":[89],"co-dimension":[91],"plane.":[94]},"counts_by_year":[],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}
