{"id":"https://openalex.org/W2011970734","doi":"https://doi.org/10.1137/080713902","title":"Invariance Entropy for Control Systems","display_name":"Invariance Entropy for Control Systems","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2011970734","doi":"https://doi.org/10.1137/080713902","mag":"2011970734"},"language":"en","primary_location":{"id":"doi:10.1137/080713902","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080713902","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":true,"oa_status":"green","oa_url":"https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-10388","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003282971","display_name":"Fritz Colonius","orcid":"https://orcid.org/0000-0003-3853-6065"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fritz Colonius","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5059120486","display_name":"Christoph Kawan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christoph Kawan","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":3.8417,"has_fulltext":false,"cited_by_count":140,"citation_normalized_percentile":{"value":0.93412181,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"48","issue":"3","first_page":"1701","last_page":"1721"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9775999784469604,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9775999784469604,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9761000275611877,"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":0.9645000100135803,"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":0.8101792931556702},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.583239734172821},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5308611989021301},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5159095525741577},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.45073404908180237},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3611992597579956},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3446323275566101},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.33856281638145447},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.22935140132904053},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11001566052436829},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.07422298192977905},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07399657368659973}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8101792931556702},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.583239734172821},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5308611989021301},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5159095525741577},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.45073404908180237},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3611992597579956},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3446323275566101},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.33856281638145447},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.22935140132904053},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11001566052436829},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.07422298192977905},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07399657368659973},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/080713902","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080713902","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"},{"id":"pmh:oai:aleph.bib-bvb.de:BVB01-020500634","is_oa":false,"landing_page_url":"https://nbn-resolving.org/urn:nbn:de:bvb:384-opus-15064","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Hochschulschrift"},{"id":"pmh:oai:aleph.bib-bvb.de:BVB01-020510853","is_oa":false,"landing_page_url":"http://opus.bibliothek.uni-augsburg.de/volltexte/2008/1333/","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Hochschulschrift"},{"id":"pmh:oai:uni-augsburg.opus-bayern.de:1210","is_oa":true,"landing_page_url":"https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-10388","pdf_url":null,"source":{"id":"https://openalex.org/S4306400930","display_name":"OPUS (Augsburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119916105","host_organization_name":"Augsburg University","host_organization_lineage":["https://openalex.org/I119916105"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"preprint"},{"id":"pmh:oai:uni-augsburg.opus-bayern.de:1357","is_oa":false,"landing_page_url":"https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/1357","pdf_url":null,"source":{"id":"https://openalex.org/S4306400930","display_name":"OPUS (Augsburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119916105","host_organization_name":"Augsburg University","host_organization_lineage":["https://openalex.org/I119916105"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"doctoralthesis"}],"best_oa_location":{"id":"pmh:oai:uni-augsburg.opus-bayern.de:1210","is_oa":true,"landing_page_url":"https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-10388","pdf_url":null,"source":{"id":"https://openalex.org/S4306400930","display_name":"OPUS (Augsburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119916105","host_organization_name":"Augsburg University","host_organization_lineage":["https://openalex.org/I119916105"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"preprint"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1484739396","https://openalex.org/W1506415348","https://openalex.org/W1572164227","https://openalex.org/W1968975267","https://openalex.org/W1978848993","https://openalex.org/W2008151824","https://openalex.org/W2063130716","https://openalex.org/W2081817659","https://openalex.org/W2096584475","https://openalex.org/W2139384666","https://openalex.org/W2157076370","https://openalex.org/W2157945087","https://openalex.org/W2470645187","https://openalex.org/W4213022453"],"related_works":["https://openalex.org/W2121543990","https://openalex.org/W2402800040","https://openalex.org/W2000020320","https://openalex.org/W4252969132","https://openalex.org/W1981078319","https://openalex.org/W2008917324","https://openalex.org/W2581541046","https://openalex.org/W4387315838","https://openalex.org/W2805799113","https://openalex.org/W2077709279"],"abstract_inverted_index":{"For":[0,42],"continuous":[1],"time":[2],"control":[3,44,48],"systems,":[4],"this":[5],"paper":[6],"introduces":[7],"invariance":[8,21,51],"entropy":[9,52],"as":[10],"a":[11],"measure":[12],"for":[13],"the":[14,28,50,56,59,63,67],"amount":[15],"of":[16,22,27,58,62,66],"information":[17],"necessary":[18],"to":[19],"achieve":[20],"weakly":[23],"invariant":[24],"compact":[25,47],"subsets":[26],"state":[29],"space.":[30],"Upper":[31],"and":[32,74],"lower":[33],"bounds":[34],"are":[35],"derived;":[36],"in":[37],"particular,":[38],"finiteness":[39],"is":[40,53,77],"proven.":[41],"linear":[43],"systems":[45],"with":[46],"range,":[49],"given":[54],"by":[55],"sum":[57],"real":[60],"parts":[61],"unstable":[64],"eigenvalues":[65],"uncontrolled":[68],"system.":[69],"A":[70],"characterization":[71],"via":[72],"covers":[73],"corresponding":[75],"feedbacks":[76],"provided.":[78]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":16},{"year":2019,"cited_by_count":14},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":16},{"year":2012,"cited_by_count":2}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}