{"id":"https://openalex.org/W2110747001","doi":"https://doi.org/10.1109/cdc.2009.5400274","title":"On positive real lemma for stabilizable and detectable systems","display_name":"On positive real lemma for stabilizable and detectable systems","publication_year":2009,"publication_date":"2009-12-01","ids":{"openalex":"https://openalex.org/W2110747001","doi":"https://doi.org/10.1109/cdc.2009.5400274","mag":"2110747001"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2009.5400274","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2009.5400274","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference","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/A5000750550","display_name":"Sadaaki Kunimatsu","orcid":null},"institutions":[{"id":"https://openalex.org/I96036126","display_name":"Kumamoto University","ror":"https://ror.org/02cgss904","country_code":"JP","type":"education","lineage":["https://openalex.org/I96036126"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Sadaaki Kunimatsu","raw_affiliation_strings":["Kumamoto University, JAPAN","Kumamoto University, Japan#TAB#"],"affiliations":[{"raw_affiliation_string":"Kumamoto University, JAPAN","institution_ids":["https://openalex.org/I96036126"]},{"raw_affiliation_string":"Kumamoto University, Japan#TAB#","institution_ids":["https://openalex.org/I96036126"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017362841","display_name":"Takao Fujii","orcid":null},"institutions":[{"id":"https://openalex.org/I125590103","display_name":"Fukui University of Technology","ror":"https://ror.org/01tm0rr86","country_code":"JP","type":"education","lineage":["https://openalex.org/I125590103"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Takao Fujii","raw_affiliation_strings":["Fukui University of Technology, JAPAN","Fukui University of Technology, Japan"],"affiliations":[{"raw_affiliation_string":"Fukui University of Technology, JAPAN","institution_ids":["https://openalex.org/I125590103"]},{"raw_affiliation_string":"Fukui University of Technology, Japan","institution_ids":["https://openalex.org/I125590103"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045053877","display_name":"Mitsuaki Ishitobi","orcid":null},"institutions":[{"id":"https://openalex.org/I96036126","display_name":"Kumamoto University","ror":"https://ror.org/02cgss904","country_code":"JP","type":"education","lineage":["https://openalex.org/I96036126"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Mitsuaki Ishitobi","raw_affiliation_strings":["Kumamoto University, JAPAN","Kumamoto University, Japan#TAB#"],"affiliations":[{"raw_affiliation_string":"Kumamoto University, JAPAN","institution_ids":["https://openalex.org/I96036126"]},{"raw_affiliation_string":"Kumamoto University, Japan#TAB#","institution_ids":["https://openalex.org/I96036126"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5000750550"],"corresponding_institution_ids":["https://openalex.org/I96036126"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.10030862,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"38","issue":null,"first_page":"4282","last_page":"4287"},"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":0.9994000196456909,"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":0.9994000196456909,"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":0.9987000226974487,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9973999857902527,"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/observability","display_name":"Observability","score":0.9300739765167236},{"id":"https://openalex.org/keywords/controllability","display_name":"Controllability","score":0.8778613805770874},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.7801640033721924},{"id":"https://openalex.org/keywords/positive-systems","display_name":"Positive systems","score":0.624620258808136},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.604396402835846},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.5735923051834106},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5095048546791077},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.49415209889411926},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4912988543510437},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4535828232765198},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4479670524597168},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4085995852947235},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3938708007335663},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3420669734477997},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20967140793800354},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20150339603424072},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.14849621057510376},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.07737284898757935},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.061881184577941895}],"concepts":[{"id":"https://openalex.org/C36299963","wikidata":"https://www.wikidata.org/wiki/Q1369844","display_name":"Observability","level":2,"score":0.9300739765167236},{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.8778613805770874},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.7801640033721924},{"id":"https://openalex.org/C2778299942","wikidata":"https://www.wikidata.org/wiki/Q7233296","display_name":"Positive systems","level":3,"score":0.624620258808136},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.604396402835846},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.5735923051834106},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5095048546791077},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.49415209889411926},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4912988543510437},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4535828232765198},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4479670524597168},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4085995852947235},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3938708007335663},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3420669734477997},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20967140793800354},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20150339603424072},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.14849621057510376},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.07737284898757935},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.061881184577941895},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"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/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2009.5400274","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2009.5400274","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.4000000059604645,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W86892992","https://openalex.org/W1570330619","https://openalex.org/W1987818455","https://openalex.org/W2010145958","https://openalex.org/W2023129790","https://openalex.org/W2030377747","https://openalex.org/W2046734354","https://openalex.org/W2046874050","https://openalex.org/W2055561145","https://openalex.org/W2077418568","https://openalex.org/W2088320060","https://openalex.org/W2101785796","https://openalex.org/W2108489060","https://openalex.org/W2128912269","https://openalex.org/W2130372034","https://openalex.org/W2159495647","https://openalex.org/W2258586177","https://openalex.org/W3195133498","https://openalex.org/W6672590579","https://openalex.org/W6691999544","https://openalex.org/W6800164818"],"related_works":["https://openalex.org/W1986570998","https://openalex.org/W2332386680","https://openalex.org/W1983142522","https://openalex.org/W2782529250","https://openalex.org/W2037921533","https://openalex.org/W2801563517","https://openalex.org/W2130864543","https://openalex.org/W2508171592","https://openalex.org/W2068126039","https://openalex.org/W2041749520"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,21,40,58],"state":[4],"the":[5,23,43,46,50,60],"positive":[6,24,51,55,61,65],"real":[7,25,52,62,66],"lemma":[8,26,53],"for":[9,27,68],"stabilizable":[10,69],"and":[11,19,63,70],"detectable":[12,71],"systems.":[13],"First,":[14],"without":[15],"assumptions":[16],"of":[17,45],"controllability":[18],"observability,":[20],"show":[22,41,59],"stable":[28],"systems":[29,72],"under":[30,73],"only":[31,74],"some":[32],"constraint":[33],"with":[34],"respect":[35],"to":[36],"invariant":[37],"zeros.":[38],"Moreover":[39],"that":[42,75],"solution":[44],"Lyapunov":[47],"equation":[48],"in":[49],"is":[54],"definite.":[56],"Next":[57],"strictly":[64],"lemmas":[67],"constraint.":[76]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
