{"id":"https://openalex.org/W2154876983","doi":"https://doi.org/10.1109/cdc.2005.1582880","title":"Causal and Stable Input/Output Structures on Multidimensional Behaviours","display_name":"Causal and Stable Input/Output Structures on Multidimensional Behaviours","publication_year":2006,"publication_date":"2006-10-04","ids":{"openalex":"https://openalex.org/W2154876983","doi":"https://doi.org/10.1109/cdc.2005.1582880","mag":"2154876983"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2005.1582880","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2005.1582880","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 44th IEEE Conference on Decision and Control","raw_type":"proceedings-article"},"type":"conference-paper","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/A5009790845","display_name":"Jeffrey J. Wood","orcid":"https://orcid.org/0000-0002-0759-6156"},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"J. Wood","raw_affiliation_strings":["School of Electronics and Computer Science, University of Southampton, Southampton, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electronics and Computer Science, University of Southampton, Southampton, UK","institution_ids":["https://openalex.org/I43439940"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023868242","display_name":"Virendra Sule","orcid":"https://orcid.org/0000-0002-7477-9673"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"V. Sule","raw_affiliation_strings":["Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081788754","display_name":"Eric Rogers","orcid":"https://orcid.org/0000-0003-0179-9398"},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"E. Rogers","raw_affiliation_strings":["School of Electronics and Computer Science, University of Southampton, Southampton, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electronics and Computer Science, University of Southampton, Southampton, UK","institution_ids":["https://openalex.org/I43439940"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"38","issue":null,"first_page":"4554","last_page":"4559"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12772","display_name":"Control and Stability of Dynamical Systems","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/causality","display_name":"Causality (physics)","score":0.8414885997772217},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.7033966779708862},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.6547656059265137},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.6303229928016663},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5640719532966614},{"id":"https://openalex.org/keywords/transfer-matrix","display_name":"Transfer matrix","score":0.5437541604042053},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.5164806842803955},{"id":"https://openalex.org/keywords/transfer-function","display_name":"Transfer function","score":0.4851139783859253},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47237351536750793},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4273003339767456},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4019048810005188},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39510706067085266},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.1878112554550171},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10240224003791809},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09735164046287537},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.06854555010795593}],"concepts":[{"id":"https://openalex.org/C64357122","wikidata":"https://www.wikidata.org/wiki/Q1149766","display_name":"Causality (physics)","level":2,"score":0.8414885997772217},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.7033966779708862},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6547656059265137},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.6303229928016663},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5640719532966614},{"id":"https://openalex.org/C122890649","wikidata":"https://www.wikidata.org/wiki/Q7834016","display_name":"Transfer matrix","level":2,"score":0.5437541604042053},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.5164806842803955},{"id":"https://openalex.org/C81299745","wikidata":"https://www.wikidata.org/wiki/Q334269","display_name":"Transfer function","level":2,"score":0.4851139783859253},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47237351536750793},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4273003339767456},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4019048810005188},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39510706067085266},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.1878112554550171},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10240224003791809},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09735164046287537},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.06854555010795593},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/cdc.2005.1582880","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2005.1582880","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 44th IEEE Conference on Decision and Control","raw_type":"proceedings-article"},{"id":"pmh:oai:eprints.soton.ac.uk:259276","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401020","display_name":"ePrints Soton (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W24811730","https://openalex.org/W614687687","https://openalex.org/W1495410784","https://openalex.org/W1538686203","https://openalex.org/W1579739595","https://openalex.org/W1599405682","https://openalex.org/W1602345739","https://openalex.org/W1891628327","https://openalex.org/W1940344321","https://openalex.org/W1973533514","https://openalex.org/W1976372728","https://openalex.org/W1985275567","https://openalex.org/W2017858648","https://openalex.org/W2029018540","https://openalex.org/W2030751899","https://openalex.org/W2035752189","https://openalex.org/W2040189394","https://openalex.org/W2043194542","https://openalex.org/W2066086134","https://openalex.org/W2067761539","https://openalex.org/W2067897288","https://openalex.org/W2077532704","https://openalex.org/W2081940784","https://openalex.org/W2088613593","https://openalex.org/W2094818292","https://openalex.org/W2146560209","https://openalex.org/W2153059745","https://openalex.org/W2160720998","https://openalex.org/W2162747898","https://openalex.org/W2176032972","https://openalex.org/W2263891311","https://openalex.org/W2493370856","https://openalex.org/W2528800419","https://openalex.org/W2610195475","https://openalex.org/W2627069115","https://openalex.org/W2738561504","https://openalex.org/W3111685920"],"related_works":["https://openalex.org/W2075768550","https://openalex.org/W3022218857","https://openalex.org/W2369178846","https://openalex.org/W2370289839","https://openalex.org/W2082716031","https://openalex.org/W2933494595","https://openalex.org/W2081494945","https://openalex.org/W4313347705","https://openalex.org/W1568049691","https://openalex.org/W2389053294"],"abstract_inverted_index":{"In":[0],"this":[1,32],"work":[2],"we":[3],"study":[4],"multidimensional":[5],"(nD)":[6],"linear":[7],"differential":[8,47],"behaviours":[9],"with":[10,29],"a":[11,20,55,80],"distinguished":[12,33],"independent":[13],"variable,":[14],"called":[15],"\"time\".":[16],"We":[17,35,61],"define":[18],"in":[19,42,66],"natural":[21],"way":[22],"causality":[23,51],"and":[24],"stability":[25],"of":[26,39,45,57,82],"input/output":[27],"structures":[28],"respect":[30],"to":[31,54],"direction.":[34],"make":[36],"an":[37],"extension":[38],"some":[40],"results":[41,64],"the":[43,58,71,83],"theory":[44],"partial":[46],"equations,":[48],"demonstrating":[49],"that":[50],"is":[52,76],"equivalent":[53],"property":[56,81],"transfer":[59,84],"matrix.":[60,85],"also":[62],"quote":[63],"which":[65],"effect":[67],"characterize":[68],"time-autonomy":[69],"for":[70],"general":[72],"systems":[73],"case.":[74],"Stability":[75],"likewise":[77],"characterized":[78],"by":[79]},"counts_by_year":[],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}