{"id":"https://openalex.org/W4413925286","doi":"https://doi.org/10.1109/tac.2025.3605299","title":"Generalized Lyapunov Conditions for K-Contraction: Analysis and Feedback Design","display_name":"Generalized Lyapunov Conditions for K-Contraction: Analysis and Feedback Design","publication_year":2025,"publication_date":"2025-09-02","ids":{"openalex":"https://openalex.org/W4413925286","doi":"https://doi.org/10.1109/tac.2025.3605299"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2025.3605299","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tac.2025.3605299","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1109/tac.2025.3605299","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003510169","display_name":"Andreu Cecilia","orcid":"https://orcid.org/0000-0002-5579-4157"},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Andreu Cecilia","raw_affiliation_strings":["Universitat Polit&#x00E8;cnica de Catalunya, Barcelona, Spain","Universitat Polit&#x00E8;cnica de Catalunya, Avinguda Diagonal, 647, Barcelona, Spain"],"raw_orcid":"https://orcid.org/0000-0002-5579-4157","affiliations":[{"raw_affiliation_string":"Universitat Polit&#x00E8;cnica de Catalunya, Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]},{"raw_affiliation_string":"Universitat Polit&#x00E8;cnica de Catalunya, Avinguda Diagonal, 647, Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047917238","display_name":"Samuele Zoboli","orcid":"https://orcid.org/0009-0006-9225-4551"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555"]},{"id":"https://openalex.org/I17866349","display_name":"Universit\u00e9 F\u00e9d\u00e9rale de Toulouse Midi-Pyr\u00e9n\u00e9es","ror":"https://ror.org/004raaa70","country_code":"FR","type":"education","lineage":["https://openalex.org/I17866349"]},{"id":"https://openalex.org/I190497903","display_name":"Laboratoire d'Analyse et d'Architecture des Syst\u00e8mes","ror":"https://ror.org/03vcm6439","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I190497903","https://openalex.org/I193033237","https://openalex.org/I196454796","https://openalex.org/I205747304","https://openalex.org/I4210095849","https://openalex.org/I4210152422","https://openalex.org/I4210159245","https://openalex.org/I4405258862","https://openalex.org/I4405259414"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Samuele Zoboli","raw_affiliation_strings":["LAAS-CNRS, Universit&#x00E9; de Toulouse, CNRS, Toulouse, France","LAAS-CNRS, Universit&#x00E9; de Toulouse, UPS, CNRS, Toulouse, France"],"raw_orcid":"https://orcid.org/0009-0006-9225-4551","affiliations":[{"raw_affiliation_string":"LAAS-CNRS, Universit&#x00E9; de Toulouse, CNRS, Toulouse, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I17866349","https://openalex.org/I190497903"]},{"raw_affiliation_string":"LAAS-CNRS, Universit&#x00E9; de Toulouse, UPS, CNRS, Toulouse, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I134560555","https://openalex.org/I17866349","https://openalex.org/I190497903"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074286208","display_name":"Daniele Astolfi","orcid":"https://orcid.org/0000-0003-2690-7420"},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210143168","display_name":"Laboratoire d'Automatique, de G\u00e9nie des Proc\u00e9d\u00e9s et de G\u00e9nie Pharmaceutique","ror":"https://ror.org/03kfjwy31","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I203339264","https://openalex.org/I4210095849","https://openalex.org/I4210143168","https://openalex.org/I59692284"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Daniele Astolfi","raw_affiliation_strings":["Universit&#x00E9; Claude Bernard Lyon 1, CNRS, LAGEPP UMR 5007, Villeurbanne, France","Universit&#x00E9; Claude Bernard Lyon 1, CNRS, LAGEPP UMR 5007, 43 boulevard du 11 novembre 1918, Villeurbanne, France"],"raw_orcid":"https://orcid.org/0000-0003-2690-7420","affiliations":[{"raw_affiliation_string":"Universit&#x00E9; Claude Bernard Lyon 1, CNRS, LAGEPP UMR 5007, Villeurbanne, France","institution_ids":["https://openalex.org/I100532134","https://openalex.org/I1294671590","https://openalex.org/I4210143168"]},{"raw_affiliation_string":"Universit&#x00E9; Claude Bernard Lyon 1, CNRS, LAGEPP UMR 5007, 43 boulevard du 11 novembre 1918, Villeurbanne, France","institution_ids":["https://openalex.org/I100532134","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046339147","display_name":"Ulysse Serres","orcid":"https://orcid.org/0000-0003-3988-3632"},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210143168","display_name":"Laboratoire d'Automatique, de G\u00e9nie des Proc\u00e9d\u00e9s et de G\u00e9nie Pharmaceutique","ror":"https://ror.org/03kfjwy31","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I203339264","https://openalex.org/I4210095849","https://openalex.org/I4210143168","https://openalex.org/I59692284"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Ulysse Serres","raw_affiliation_strings":["Universit&#x00E9; Claude Bernard Lyon 1, CNRS, LAGEPP UMR 5007, Villeurbanne, France","Universit&#x00E9; Claude Bernard Lyon 1, CNRS, LAGEPP UMR 5007, 43 boulevard du 11 novembre 1918, Villeurbanne, France"],"raw_orcid":"https://orcid.org/0000-0003-3988-3632","affiliations":[{"raw_affiliation_string":"Universit&#x00E9; Claude Bernard Lyon 1, CNRS, LAGEPP UMR 5007, Villeurbanne, France","institution_ids":["https://openalex.org/I100532134","https://openalex.org/I1294671590","https://openalex.org/I4210143168"]},{"raw_affiliation_string":"Universit&#x00E9; Claude Bernard Lyon 1, CNRS, LAGEPP UMR 5007, 43 boulevard du 11 novembre 1918, Villeurbanne, France","institution_ids":["https://openalex.org/I100532134","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082790000","display_name":"Vincent Andrieu","orcid":"https://orcid.org/0000-0003-1877-6205"},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210143168","display_name":"Laboratoire d'Automatique, de G\u00e9nie des Proc\u00e9d\u00e9s et de G\u00e9nie Pharmaceutique","ror":"https://ror.org/03kfjwy31","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I203339264","https://openalex.org/I4210095849","https://openalex.org/I4210143168","https://openalex.org/I59692284"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Vincent Andrieu","raw_affiliation_strings":["Universit&#x00E9; Claude Bernard Lyon 1, CNRS, LAGEPP UMR 5007, Villeurbanne, France","Universit&#x00E9; Claude Bernard Lyon 1, CNRS, LAGEPP UMR 5007, 43 boulevard du 11 novembre 1918, Villeurbanne, France"],"raw_orcid":"https://orcid.org/0000-0003-1877-6205","affiliations":[{"raw_affiliation_string":"Universit&#x00E9; Claude Bernard Lyon 1, CNRS, LAGEPP UMR 5007, Villeurbanne, France","institution_ids":["https://openalex.org/I100532134","https://openalex.org/I1294671590","https://openalex.org/I4210143168"]},{"raw_affiliation_string":"Universit&#x00E9; Claude Bernard Lyon 1, CNRS, LAGEPP UMR 5007, 43 boulevard du 11 novembre 1918, Villeurbanne, France","institution_ids":["https://openalex.org/I100532134","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":7,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.21381573,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"71","issue":"2","first_page":"1022","last_page":"1037"},"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":0.9983000159263611,"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":0.9983000159263611,"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":0.9689000248908997,"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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9574999809265137,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6153957843780518},{"id":"https://openalex.org/keywords/contraction","display_name":"Contraction (grammar)","score":0.5996092557907104},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5449019074440002},{"id":"https://openalex.org/keywords/feedback-control","display_name":"Feedback control","score":0.4855901598930359},{"id":"https://openalex.org/keywords/lyapunov-redesign","display_name":"Lyapunov redesign","score":0.4619067311286926},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4251844584941864},{"id":"https://openalex.org/keywords/output-feedback","display_name":"Output feedback","score":0.4190012514591217},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4080072343349457},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3648151159286499},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.3533443212509155},{"id":"https://openalex.org/keywords/control-engineering","display_name":"Control engineering","score":0.334155797958374},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.1849219799041748},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.17337578535079956},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15384119749069214},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.14846846461296082},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08368474245071411}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6153957843780518},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.5996092557907104},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5449019074440002},{"id":"https://openalex.org/C3018651601","wikidata":"https://www.wikidata.org/wiki/Q183635","display_name":"Feedback control","level":2,"score":0.4855901598930359},{"id":"https://openalex.org/C37935115","wikidata":"https://www.wikidata.org/wiki/Q6707085","display_name":"Lyapunov redesign","level":4,"score":0.4619067311286926},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4251844584941864},{"id":"https://openalex.org/C3018623182","wikidata":"https://www.wikidata.org/wiki/Q154021","display_name":"Output feedback","level":3,"score":0.4190012514591217},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4080072343349457},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3648151159286499},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.3533443212509155},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.334155797958374},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.1849219799041748},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.17337578535079956},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15384119749069214},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.14846846461296082},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08368474245071411},{"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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.0},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tac.2025.3605299","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tac.2025.3605299","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:upcommons.upc.edu:2117/456383","is_oa":true,"landing_page_url":"https://hdl.handle.net/2117/456383","pdf_url":null,"source":{"id":"https://openalex.org/S4377196262","display_name":"UPCommons institutional repository (Universitat Polit\u00e8cnica de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9617848","host_organization_name":"Universitat Polit\u00e8cnica de Catalunya","host_organization_lineage":["https://openalex.org/I9617848"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:HAL:hal-04300588v3","is_oa":false,"landing_page_url":"https://hal.science/hal-04300588","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Automatic Control, In press, &#x27E8;10.1109/TAC.2025.3605299&#x27E9;","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1109/tac.2025.3605299","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tac.2025.3605299","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G206775298","display_name":"In_x000C_finite dimensional internal model regulators for fi_x000C_nite dimensional systems","funder_award_id":"ANR-22-CE48-0009","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G2384274448","display_name":"Data and Prior, Machine Learning and Control","funder_award_id":"ANR-19-CE23-0006","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2349796700","https://openalex.org/W1964805920","https://openalex.org/W3194517843","https://openalex.org/W3217133416","https://openalex.org/W2234502090","https://openalex.org/W4388874082","https://openalex.org/W2147929414","https://openalex.org/W2496188264","https://openalex.org/W2383986032","https://openalex.org/W1979419366"],"abstract_inverted_index":{"Recently,":[0],"the":[1,17,27,48,77,93,96,107],"concept":[2],"of$k$-contraction":[3,19],"has":[4,21],"been":[5],"introduced":[6],"as":[7],"a":[8,37,87],"promising":[9],"generalization":[10],"of":[11],"contraction":[12],"for":[13,91],"dynamical":[14],"systems.":[15],"However,":[16],"study":[18],"properties":[20,105],"faced":[22],"significant":[23],"challenges":[24],"due":[25],"to":[26,45,103],"reliance":[28],"on":[29,82,106],"complex":[30],"mathematical":[31],"objects":[32],"called":[33],"matrix":[34,67],"compounds.":[35],"As":[36],"result,":[38],"related":[39],"control":[40],"design":[41,89],"methodologies":[42],"have":[43],"yet":[44],"appear":[46],"in":[47,76],"literature.":[49],"In":[50],"this":[51],"paper,":[52],"we":[53,85],"overcome":[54],"existing":[55],"limitations":[56],"and":[57,95],"propose":[58,86],"new":[59],"sufficient":[60],"conditions":[61,72],"for$k$-contraction":[62],"which":[63,99],"do":[64],"not":[65],"require":[66],"compounds":[68],"computation.":[69],"Notably,":[70],"these":[71,83],"are":[73],"also":[74],"necessary":[75],"linear":[78,94],"time-invariant":[79],"framework.":[80],"Building":[81],"findings,":[84],"feedback":[88],"methodology":[90],"both":[92],"nonlinear":[97],"scenarios":[98],"can":[100],"be":[101],"used":[102],"enforce$k$-contractivity":[104],"closed-loop":[108],"dynamics.":[109]},"counts_by_year":[],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-09-03T00:00:00"}
