{"id":"https://openalex.org/W3138402147","doi":"https://doi.org/10.1137/21m1404685","title":"Internally Hankel $k$-Positive Systems","display_name":"Internally Hankel $k$-Positive Systems","publication_year":2022,"publication_date":"2022-08-01","ids":{"openalex":"https://openalex.org/W3138402147","doi":"https://doi.org/10.1137/21m1404685","mag":"3138402147"},"language":"en","primary_location":{"id":"doi:10.1137/21m1404685","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1404685","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","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/A5077723724","display_name":"Christian Gru\u00dfler","orcid":"https://orcid.org/0000-0003-2437-3154"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christian Grussler","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-2437-3154","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076102992","display_name":"Thiago B. Burghi","orcid":"https://orcid.org/0000-0001-7416-3433"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Thiago Burghi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5072786751","display_name":"Somayeh Sojoudi","orcid":"https://orcid.org/0000-0001-7177-7712"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Somayeh Sojoudi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7846,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.67267766,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"60","issue":"4","first_page":"2373","last_page":"2392"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9995999932289124,"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/T11236","display_name":"Control Systems and Identification","score":0.9991999864578247,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9980999827384949,"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/mathematics","display_name":"Mathematics","score":0.7759597897529602},{"id":"https://openalex.org/keywords/controllability","display_name":"Controllability","score":0.7302443981170654},{"id":"https://openalex.org/keywords/observability","display_name":"Observability","score":0.6902995705604553},{"id":"https://openalex.org/keywords/hankel-matrix","display_name":"Hankel matrix","score":0.6499506235122681},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5689124464988708},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.4919538199901581},{"id":"https://openalex.org/keywords/positive-systems","display_name":"Positive systems","score":0.4678018391132355},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4519783854484558},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4263276755809784},{"id":"https://openalex.org/keywords/variation-of-parameters","display_name":"Variation of parameters","score":0.4113101363182068},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.39086565375328064},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3468359410762787},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3289855122566223},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30533212423324585},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.12465247511863708},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.12375333905220032},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1109146773815155},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07727512717247009}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7759597897529602},{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.7302443981170654},{"id":"https://openalex.org/C36299963","wikidata":"https://www.wikidata.org/wiki/Q1369844","display_name":"Observability","level":2,"score":0.6902995705604553},{"id":"https://openalex.org/C25023664","wikidata":"https://www.wikidata.org/wiki/Q1575637","display_name":"Hankel matrix","level":2,"score":0.6499506235122681},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5689124464988708},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.4919538199901581},{"id":"https://openalex.org/C2778299942","wikidata":"https://www.wikidata.org/wiki/Q7233296","display_name":"Positive systems","level":3,"score":0.4678018391132355},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4519783854484558},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4263276755809784},{"id":"https://openalex.org/C62689967","wikidata":"https://www.wikidata.org/wiki/Q1205942","display_name":"Variation of parameters","level":3,"score":0.4113101363182068},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39086565375328064},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3468359410762787},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3289855122566223},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30533212423324585},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.12465247511863708},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.12375333905220032},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1109146773815155},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07727512717247009},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m1404685","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1404685","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G345821319","display_name":null,"funder_award_id":"n.670645","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"},{"id":"https://openalex.org/G3553340086","display_name":null,"funder_award_id":"PAPIIT RA105518","funder_id":"https://openalex.org/F4320335100","funder_display_name":"Direcci\u00f3n General de Asuntos del Personal Acad\u00e9mico, Universidad Nacional Aut\u00f3noma de M\u00e9xico"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320335100","display_name":"Direcci\u00f3n General de Asuntos del Personal Acad\u00e9mico, Universidad Nacional Aut\u00f3noma de M\u00e9xico","ror":"https://ror.org/01tmp8f25"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"},{"id":"https://openalex.org/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W565573710","https://openalex.org/W1500921805","https://openalex.org/W1529274881","https://openalex.org/W1534430411","https://openalex.org/W1551480811","https://openalex.org/W1606815384","https://openalex.org/W1623874669","https://openalex.org/W1736530648","https://openalex.org/W1763790326","https://openalex.org/W1965014941","https://openalex.org/W1965567178","https://openalex.org/W1983868185","https://openalex.org/W1991579213","https://openalex.org/W1998121032","https://openalex.org/W2003716359","https://openalex.org/W2021317570","https://openalex.org/W2042700920","https://openalex.org/W2073540225","https://openalex.org/W2076977679","https://openalex.org/W2101037112","https://openalex.org/W2119886894","https://openalex.org/W2145067072","https://openalex.org/W2147741970","https://openalex.org/W2559961335","https://openalex.org/W2591400162","https://openalex.org/W2610279013","https://openalex.org/W2610857016","https://openalex.org/W2676772757","https://openalex.org/W2788147144","https://openalex.org/W2949792757","https://openalex.org/W2962957436","https://openalex.org/W2997976910","https://openalex.org/W3005724979","https://openalex.org/W3012599641","https://openalex.org/W3017077461","https://openalex.org/W3036048774","https://openalex.org/W3037221844","https://openalex.org/W3091085714","https://openalex.org/W3100328195","https://openalex.org/W3101349374","https://openalex.org/W3104452722","https://openalex.org/W3185635697","https://openalex.org/W3204353742","https://openalex.org/W3214804586","https://openalex.org/W4206002127","https://openalex.org/W4206595925","https://openalex.org/W4214758613","https://openalex.org/W4229706427","https://openalex.org/W4235143360","https://openalex.org/W4246149624","https://openalex.org/W4396951526"],"related_works":["https://openalex.org/W2576505995","https://openalex.org/W2540358353","https://openalex.org/W2375752689","https://openalex.org/W2049542879","https://openalex.org/W1594253023","https://openalex.org/W104284319","https://openalex.org/W1607432268","https://openalex.org/W1602214408","https://openalex.org/W2096295504","https://openalex.org/W2435330674"],"abstract_inverted_index":{"There":[0],"has":[1,88],"been":[2,31,89],"an":[3,228],"increased":[4],"interest":[5],"in":[6,190,245],"the":[7,34,48,62,74,86,91,100,103,108,117,127,130,158,166,191,197,216,239,246,267],"variation":[8,64,101,222],"diminishing":[9,223],"properties":[10,28],"of":[11,37,50,77,94,102,120,135,169,193,196,221,241,249,269],"controlled":[12,24,224],"linear":[13,19,82,225],"time-invariant":[14],"(LTI)":[15],"systems":[16,20,42,83,149],"and":[17,111,132,152,172,181,214,243],"time-varying":[18],"without":[21,84],"inputs.":[22],"In":[23,107],"LTI":[25,109,148,250],"systems,":[26,142],"these":[27],"have":[29,43],"recently":[30],"studied":[32],"from":[33,55],"external":[35,133,170,211],"perspective":[36,93],"$k$-positive":[38,95,141,273],"Hankel":[39,44,140,171,179,212,272],"operators.":[40],"Such":[41],"operators":[45,154],"that":[46,165],"diminish":[47,99],"number":[49,240],"sign":[51],"changes":[52],"(the":[53],"variation)":[54],"past":[56],"input":[57,63],"to":[58,116,209,234],"future":[59,219],"output":[60],"if":[61],"is":[65],"at":[66],"most":[67],"$k-1$.":[68],"For":[69,81],"$k=1$,":[70,113],"this":[71,114,188,204],"coincides":[72],"with":[73],"classical":[75,118],"class":[76,119,205],"externally":[78],"positive":[79,122,258],"systems.":[80,123,201,226,251],"inputs,":[85],"focus":[87],"on":[90],"internal":[92,131,173,178,194],"state-transition":[96,159],"matrices,":[97],"which":[98,143],"initial":[104],"system":[105],"state.":[106],"case":[110],"for":[112,186,218,238,266],"corresponds":[115],"(unforced)":[121],"This":[124],"paper":[125],"bridges":[126],"gap":[128],"between":[129],"perspectives":[134],"$k$-positivity":[136,174],"by":[137],"analyzing":[138],"internally":[139,271],"we":[144,182,230,261],"define":[145],"as":[146,155,157],"state-space":[147],"where":[150],"controllability":[151],"observability":[153],"well":[156],"matrix":[160],"are":[161,175],"$k$-positive.":[162],"We":[163],"show":[164],"existing":[167],"notions":[168],"subsumed":[176],"under":[177],"$k$-positivity,":[180,213],"derive":[183,235],"tractable":[184],"conditions":[185,265],"verifying":[187],"property":[189],"form":[192],"positivity":[195],"first":[198],"$k$":[199],"compound":[200],"As":[202,227],"such,":[203],"provides":[206],"new":[207,236,257],"means":[208],"verify":[210],"lays":[215],"foundation":[217],"investigations":[220],"application,":[229],"use":[231],"our":[232,253],"framework":[233],"bounds":[237],"over-":[242],"undershoots":[244],"step":[247],"responses":[248],"Since":[252],"characterization":[254],"defines":[255],"a":[256],"realization":[259],"problem,":[260],"also":[262],"discuss":[263],"geometric":[264],"existence":[268],"minimal":[270],"realizations.":[274]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}