{"id":"https://openalex.org/W3162230888","doi":"https://doi.org/10.1109/tac.2022.3177715","title":"A Sufficient Condition for $k$-Contraction of the Series Connection of Two Systems","display_name":"A Sufficient Condition for $k$-Contraction of the Series Connection of Two Systems","publication_year":2022,"publication_date":"2022-05-26","ids":{"openalex":"https://openalex.org/W3162230888","doi":"https://doi.org/10.1109/tac.2022.3177715","mag":"3162230888"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2022.3177715","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2022.3177715","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2105.07678","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034486968","display_name":"Ron Ofir","orcid":"https://orcid.org/0000-0003-0611-3279"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Ron Ofir","raw_affiliation_strings":["Andrew and Erna Viterbi Faculty of Electrical Engineering, Technion&#x2014;Israel Institute of Technology, Haifa, Israel"],"affiliations":[{"raw_affiliation_string":"Andrew and Erna Viterbi Faculty of Electrical Engineering, Technion&#x2014;Israel Institute of Technology, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074869481","display_name":"Michael Margaliot","orcid":"https://orcid.org/0000-0001-8319-8996"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Michael Margaliot","raw_affiliation_strings":["School of Electrical Engineering Sagol School of Neuroscience, Tel-Aviv University, Tel-Aviv, Israel"],"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering Sagol School of Neuroscience, Tel-Aviv University, Tel-Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067412613","display_name":"Yoash Levron","orcid":"https://orcid.org/0000-0001-9775-1406"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Yoash Levron","raw_affiliation_strings":["Andrew and Erna Viterbi Faculty of Electrical Engineering, Technion&#x2014;Israel Institute of Technology, Haifa, Israel"],"affiliations":[{"raw_affiliation_string":"Andrew and Erna Viterbi Faculty of Electrical Engineering, Technion&#x2014;Israel Institute of Technology, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044026747","display_name":"Jean-Jacques Slotine","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jean-Jacques Slotine","raw_affiliation_strings":["Department of Mechanical Engineering Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, MA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5034486968"],"corresponding_institution_ids":["https://openalex.org/I174306211"],"apc_list":null,"apc_paid":null,"fwci":2.3031,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.87560177,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"67","issue":"9","first_page":"4994","last_page":"5001"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9991999864578247,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9991999864578247,"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":0.9666000008583069,"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/T10223","display_name":"Microgrid Control and Optimization","score":0.9359999895095825,"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/notation","display_name":"Notation","score":0.7417963743209839},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46278125047683716},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.36657536029815674},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3442443013191223},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34350883960723877},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32265937328338623},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.23919588327407837},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.20033541321754456}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.7417963743209839},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46278125047683716},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36657536029815674},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3442443013191223},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34350883960723877},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32265937328338623},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.23919588327407837},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.20033541321754456}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tac.2022.3177715","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2022.3177715","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2105.07678","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2105.07678","pdf_url":"https://arxiv.org/pdf/2105.07678","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2105.07678","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2105.07678","pdf_url":"https://arxiv.org/pdf/2105.07678","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W26528315","https://openalex.org/W80276240","https://openalex.org/W391578156","https://openalex.org/W1488435683","https://openalex.org/W1532095972","https://openalex.org/W1543420164","https://openalex.org/W1603022741","https://openalex.org/W1688253628","https://openalex.org/W1965360919","https://openalex.org/W1965567178","https://openalex.org/W1970592681","https://openalex.org/W1975348634","https://openalex.org/W1977291814","https://openalex.org/W1984819558","https://openalex.org/W2008072444","https://openalex.org/W2015745168","https://openalex.org/W2036216368","https://openalex.org/W2042371484","https://openalex.org/W2049546703","https://openalex.org/W2056706729","https://openalex.org/W2089171051","https://openalex.org/W2094935658","https://openalex.org/W2118430238","https://openalex.org/W2127340456","https://openalex.org/W2128978199","https://openalex.org/W2132185311","https://openalex.org/W2134889984","https://openalex.org/W2136351630","https://openalex.org/W2312834382","https://openalex.org/W2312915715","https://openalex.org/W2599892769","https://openalex.org/W2952706871","https://openalex.org/W2962957436","https://openalex.org/W2963571180","https://openalex.org/W3005724979","https://openalex.org/W3012278824","https://openalex.org/W3012599641","https://openalex.org/W3017077461","https://openalex.org/W3027413213","https://openalex.org/W3038900894","https://openalex.org/W3098306608","https://openalex.org/W3100328195","https://openalex.org/W3108963777","https://openalex.org/W3114757943","https://openalex.org/W3141785485","https://openalex.org/W3143337168","https://openalex.org/W3153305782","https://openalex.org/W3204353742","https://openalex.org/W3214804586","https://openalex.org/W4210452658","https://openalex.org/W4220903325","https://openalex.org/W4240241701","https://openalex.org/W6631893366","https://openalex.org/W6637480540","https://openalex.org/W6809331532"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2051487156","https://openalex.org/W2504004674","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027"],"abstract_inverted_index":{"The":[0],"flow":[1],"of":[2,48,55,79,106,114,136],"an":[3,59,118,128],"<inline-formula":[4,9,16,24,31,83,97],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[5,10,17,25,32,84,98],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex-math":[6,11,18,26,33,85,99],"notation=\"LaTeX\">$n$</tex-math></inline-formula>":[7],"-dimensional":[8,28],"notation=\"LaTeX\">$k$</tex-math></inline-formula>":[12,27,86,100],"-contracting":[13],"system,":[14],"with":[15,127],"notation=\"LaTeX\">$k\\in":[19],"\\lbrace":[20],"1,\\ldots,n\\rbrace$</tex-math></inline-formula>":[21],",":[22,35],"contracts":[23],"parallelotopes.":[29],"For":[30],"notation=\"LaTeX\">$k=1$</tex-math></inline-formula>":[34],"this":[36],"reduces":[37],"to":[38],"a":[39,66,92,107],"standard":[40],"contracting":[41,56],"system.":[42,62],"One":[43],"reason":[44],"for":[45,95],"the":[46,72,76,96,133],"usefulness":[47],"1-contracting":[49,61],"systems":[50,126],"is":[51,82,89],"that":[52,71,124],"many":[53],"interconnections":[54],"subsystems":[57,81],"yield":[58],"overall":[60],"Here,":[63],"we":[64,120],"derive":[65],"new":[67,93],"sufficient":[68],"condition":[69],"guaranteeing":[70,123],"system":[73],"obtained":[74],"from":[75],"series":[77],"interconnection":[78],"two":[80],"-contracting.":[87],"This":[88],"based":[90],"on":[91],"formula":[94],"th":[101],"multiplicative":[102],"and":[103],"additive":[104],"compounds":[105],"block-diagonal":[108],"matrix":[109],"(BDM),":[110],"which":[111],"may":[112],"be":[113],"independent":[115],"interest.":[116],"As":[117],"application,":[119],"find":[121],"conditions":[122],"2-contracting":[125,138],"exponentially":[129],"decaying":[130],"input":[131],"retain":[132],"well-ordered":[134],"behavior":[135],"time-invariant":[137],"systems.":[139]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-03-27T14:29:43.386196","created_date":"2021-05-24T00:00:00"}
