{"id":"https://openalex.org/W4391389402","doi":"https://doi.org/10.1137/23m1551225","title":"A Stability Dichotomy for Discrete-Time Linear Switching Systems in Dimension Two","display_name":"A Stability Dichotomy for Discrete-Time Linear Switching Systems in Dimension Two","publication_year":2024,"publication_date":"2024-01-31","ids":{"openalex":"https://openalex.org/W4391389402","doi":"https://doi.org/10.1137/23m1551225"},"language":"en","primary_location":{"id":"doi:10.1137/23m1551225","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1551225","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/A5031050575","display_name":"Ian D. Morris","orcid":"https://orcid.org/0000-0001-7826-459X"},"institutions":[{"id":"https://openalex.org/I166337079","display_name":"Queen Mary University of London","ror":"https://ror.org/026zzn846","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I166337079"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Ian D. Morris","raw_affiliation_strings":["School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, UK"],"raw_orcid":"https://orcid.org/0000-0001-7826-459X","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, UK","institution_ids":["https://openalex.org/I166337079"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5031050575"],"corresponding_institution_ids":["https://openalex.org/I166337079"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0084774,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"62","issue":"1","first_page":"400","last_page":"414"},"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":0.9980000257492065,"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":0.9980000257492065,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9962000250816345,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.992900013923645,"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":0.8801220059394836},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6913233995437622},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5800644755363464},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.45416054129600525},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35705113410949707},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.343044638633728},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33459264039993286},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.09518364071846008}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8801220059394836},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6913233995437622},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5800644755363464},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.45416054129600525},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35705113410949707},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.343044638633728},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33459264039993286},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.09518364071846008},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/23m1551225","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1551225","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/G382211468","display_name":null,"funder_award_id":"RPG-2016-194","funder_id":"https://openalex.org/F4320319993","funder_display_name":"Leverhulme Trust"}],"funders":[{"id":"https://openalex.org/F4320319993","display_name":"Leverhulme Trust","ror":"https://ror.org/012mzw131"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1622830285","https://openalex.org/W1683991801","https://openalex.org/W1966469345","https://openalex.org/W1991656001","https://openalex.org/W2018515222","https://openalex.org/W2020979852","https://openalex.org/W2051710605","https://openalex.org/W2060886109","https://openalex.org/W2105979036","https://openalex.org/W2116656166","https://openalex.org/W2133979039","https://openalex.org/W2963427409","https://openalex.org/W3216050420","https://openalex.org/W4238257903","https://openalex.org/W4381490429"],"related_works":["https://openalex.org/W1987895267","https://openalex.org/W2350519135","https://openalex.org/W2390619334","https://openalex.org/W2052190160","https://openalex.org/W2375327612","https://openalex.org/W1502126983","https://openalex.org/W2365099857","https://openalex.org/W4297848888","https://openalex.org/W2347365352","https://openalex.org/W2360419795"],"abstract_inverted_index":{".We":[0],"prove":[1],"that,":[2],"for":[3,58,74],"every":[4],"discrete-time":[5],"linear":[6,37,83],"switching":[7,17,79,81],"system":[8,21],"in":[9,60,70],"two":[10,49,61],"complex":[11],"variables":[12,63],"and":[13,73],"with":[14,34,76],"finitely":[15],"many":[16,78],"states,":[18],"either":[19],"the":[20],"is":[22,65],"Lyapunov":[23],"stable":[24],"or":[25],"there":[26],"exists":[27],"a":[28,42],"trajectory":[29],"which":[30],"escapes":[31],"to":[32,46,56,67],"infinity":[33],"at":[35],"least":[36],"speed.":[38],"We":[39],"also":[40],"give":[41],"checkable":[43],"algebraic":[44],"criterion":[45],"distinguish":[47],"these":[48],"cases.":[50],"This":[51],"dichotomy":[52],"was":[53],"previously":[54],"known":[55,66],"hold":[57],"systems":[59,75],"real":[62],"but":[64],"be":[68],"false":[69],"higher":[71],"dimensions":[72],"infinitely":[77],"states.Keywordslinear":[80],"systemdiscrete":[82],"inclusionjoint":[84],"spectral":[85],"radiusmarginal":[86],"stabilitymarginal":[87],"instabilityMSC":[88],"codes15A9993C30":[89]},"counts_by_year":[],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
