{"id":"https://openalex.org/W2135128809","doi":"https://doi.org/10.1109/cdc.2007.4434084","title":"Reachability analysis of linear systems with uncertain parameters and inputs","display_name":"Reachability analysis of linear systems with uncertain parameters and inputs","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2135128809","doi":"https://doi.org/10.1109/cdc.2007.4434084","mag":"2135128809"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2007.4434084","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2007.4434084","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 46th IEEE Conference on Decision and Control","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://mediatum.ub.tum.de/1289985","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005383495","display_name":"Matthias Althoff","orcid":"https://orcid.org/0000-0003-3733-842X"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Matthias Althoff","raw_affiliation_strings":["Institute of Automatic Control Engineering, Technische Universit\u00e4t M\u00fcnchen, Munchen, Germany","Tech. Univ. Munchen, Munchen"],"affiliations":[{"raw_affiliation_string":"Institute of Automatic Control Engineering, Technische Universit\u00e4t M\u00fcnchen, Munchen, Germany","institution_ids":["https://openalex.org/I62916508"]},{"raw_affiliation_string":"Tech. Univ. Munchen, Munchen","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040756775","display_name":"Olaf Stursberg","orcid":"https://orcid.org/0000-0002-9600-457X"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Olaf Stursberg","raw_affiliation_strings":["Institute of Automatic Control Engineering, Technische Universit\u00e4t M\u00fcnchen, Munchen, Germany","Tech. Univ. Munchen, Munchen"],"affiliations":[{"raw_affiliation_string":"Institute of Automatic Control Engineering, Technische Universit\u00e4t M\u00fcnchen, Munchen, Germany","institution_ids":["https://openalex.org/I62916508"]},{"raw_affiliation_string":"Tech. Univ. Munchen, Munchen","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081223790","display_name":"Martin Buss","orcid":"https://orcid.org/0000-0002-1776-2752"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martin Buss","raw_affiliation_strings":["Institute of Automatic Control Engineering, Technische Universit\u00e4t M\u00fcnchen, Munchen, Germany","Tech. Univ. Munchen, Munchen"],"affiliations":[{"raw_affiliation_string":"Institute of Automatic Control Engineering, Technische Universit\u00e4t M\u00fcnchen, Munchen, Germany","institution_ids":["https://openalex.org/I62916508"]},{"raw_affiliation_string":"Tech. Univ. Munchen, Munchen","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5005383495"],"corresponding_institution_ids":["https://openalex.org/I62916508"],"apc_list":null,"apc_paid":null,"fwci":4.1093,"has_fulltext":false,"cited_by_count":90,"citation_normalized_percentile":{"value":0.93999438,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"726","last_page":"732"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10142","display_name":"Formal Methods in Verification","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.9932000041007996,"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/T11125","display_name":"Petri Nets in System Modeling","score":0.9926000237464905,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/reachability","display_name":"Reachability","score":0.9596973657608032},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.814922571182251},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6792532801628113},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6128085255622864},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5935717821121216},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.590715765953064},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5131112337112427},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.46747609972953796},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39960455894470215},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3543429374694824},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3433389663696289},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3244864344596863},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.28856927156448364},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.10671505331993103},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07498866319656372},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.059572845697402954}],"concepts":[{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.9596973657608032},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.814922571182251},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6792532801628113},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6128085255622864},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5935717821121216},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.590715765953064},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5131112337112427},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.46747609972953796},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39960455894470215},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3543429374694824},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3433389663696289},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3244864344596863},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28856927156448364},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.10671505331993103},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07498866319656372},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.059572845697402954},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/cdc.2007.4434084","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2007.4434084","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 46th IEEE Conference on Decision and Control","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.149.260","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.149.260","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.lsr.ei.tum.de/fileadmin/publications/CDC07.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.668.2596","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.668.2596","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www6.in.tum.de/Main/Publications/Althoff2007c.pdf","raw_type":"text"},{"id":"pmh:oai:mediatum.ub.tum.de:node/1289985","is_oa":true,"landing_page_url":"https://mediatum.ub.tum.de/1289985","pdf_url":null,"source":{"id":"https://openalex.org/S4377196330","display_name":"mediaTUM  (Technical University of Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"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":"ConferencePaper"}],"best_oa_location":{"id":"pmh:oai:mediatum.ub.tum.de:node/1289985","is_oa":true,"landing_page_url":"https://mediatum.ub.tum.de/1289985","pdf_url":null,"source":{"id":"https://openalex.org/S4377196330","display_name":"mediaTUM  (Technical University of Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"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":"ConferencePaper"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1499853177","https://openalex.org/W1522694098","https://openalex.org/W1525967073","https://openalex.org/W1542938996","https://openalex.org/W1569692898","https://openalex.org/W1726255445","https://openalex.org/W1987664276","https://openalex.org/W2106565812","https://openalex.org/W2110910849","https://openalex.org/W2115796899","https://openalex.org/W2119768731","https://openalex.org/W2131441094","https://openalex.org/W2138401518","https://openalex.org/W2145201569","https://openalex.org/W2157832650","https://openalex.org/W2160960061","https://openalex.org/W2483775066","https://openalex.org/W6681835926"],"related_works":["https://openalex.org/W4300463216","https://openalex.org/W2164153476","https://openalex.org/W2774442510","https://openalex.org/W4375851942","https://openalex.org/W2142388326","https://openalex.org/W1996190563","https://openalex.org/W2059046304","https://openalex.org/W2144878166","https://openalex.org/W2119819375","https://openalex.org/W2295922520"],"abstract_inverted_index":{"For":[0],"a":[1,27,78,83],"dynamic":[2],"system":[3,41,54],"with":[4,39,56],"given":[5],"initial":[6],"state":[7,11],"set,":[8],"the":[9,14],"reachable":[10,34,66],"set":[12],"contains":[13],"states":[15],"along":[16],"all":[17],"possible":[18],"trajectories":[19],"defined":[20],"over":[21],"(in-)flnite":[22],"time.":[23],"This":[24],"paper":[25],"presents":[26],"method":[28],"for":[29,36,51],"computing":[30],"conservative":[31],"approximations":[32],"of":[33,53,71,80],"sets":[35,67],"linear":[37],"systems":[38],"uncertain":[40],"matrices":[42,55],"and":[43,47],"bounded":[44,60],"inputs.":[45],"Over-":[46],"under-approximations":[48],"are":[49],"computed":[50,75],"exponentials":[52],"entries":[57],"specified":[58],"as":[59],"intervals.":[61],"It":[62],"is":[63],"shown":[64],"that":[65],"represented":[68],"by":[69],"sequences":[70],"zonotopes":[72],"can":[73],"be":[74],"up":[76],"to":[77],"dimension":[79],"100":[81],"within":[82],"few":[84],"seconds.":[85]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":16},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}