{"id":"https://openalex.org/W4386518024","doi":"https://doi.org/10.1155/2023/7564084","title":"Practical Input-to-State Stability of Nonlinear Systems with Time Delay","display_name":"Practical Input-to-State Stability of Nonlinear Systems with Time Delay","publication_year":2023,"publication_date":"2023-09-07","ids":{"openalex":"https://openalex.org/W4386518024","doi":"https://doi.org/10.1155/2023/7564084"},"language":"en","primary_location":{"id":"doi:10.1155/2023/7564084","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2023/7564084","pdf_url":"https://downloads.hindawi.com/journals/complexity/2023/7564084.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/complexity/2023/7564084.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010661035","display_name":"Abdellatif Ben Makhlouf","orcid":"https://orcid.org/0000-0001-7142-7026"},"institutions":[{"id":"https://openalex.org/I142899784","display_name":"University of Sfax","ror":"https://ror.org/04d4sd432","country_code":"TN","type":"education","lineage":["https://openalex.org/I142899784"]}],"countries":["TN"],"is_corresponding":true,"raw_author_name":"Abdellatif Ben Makhlouf","raw_affiliation_strings":["Department of Mathematics, Faculty of Sciences of Sfax, Sfax University, BP 1171, Sfax, Tunisia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Sciences of Sfax, Sfax University, BP 1171, Sfax, Tunisia","institution_ids":["https://openalex.org/I142899784"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055967546","display_name":"Nizar Hadj Taieb","orcid":"https://orcid.org/0000-0003-2761-1402"},"institutions":[{"id":"https://openalex.org/I142899784","display_name":"University of Sfax","ror":"https://ror.org/04d4sd432","country_code":"TN","type":"education","lineage":["https://openalex.org/I142899784"]}],"countries":["TN"],"is_corresponding":false,"raw_author_name":"Nizar Hadj Taieb","raw_affiliation_strings":["Department of Mathematics, Faculty of Sciences of Sfax, Sfax University, BP 1171, Sfax, Tunisia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Sciences of Sfax, Sfax University, BP 1171, Sfax, Tunisia","institution_ids":["https://openalex.org/I142899784"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021520660","display_name":"Mohamed Rhaima","orcid":"https://orcid.org/0000-0002-2400-9275"},"institutions":[{"id":"https://openalex.org/I28022161","display_name":"King Saud University","ror":"https://ror.org/02f81g417","country_code":"SA","type":"education","lineage":["https://openalex.org/I28022161"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Mohamed Rhaima","raw_affiliation_strings":["Department of Statistics and Operations Research, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Statistics and Operations Research, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]}]},{"author_position":"last","author":{"id":null,"display_name":"Lassaad Mchiri","orcid":"https://orcid.org/0000-0001-8306-201X"},"institutions":[{"id":"https://openalex.org/I4210097372","display_name":"\u00c9cole Nationale Sup\u00e9rieure d\u2019Informatique pour l\u2019Industrie et l\u2019Entreprise","ror":"https://ror.org/00tx98v53","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210097372"]},{"id":"https://openalex.org/I88467170","display_name":"Universit\u00e9 d'\u00c9vry Val-d'Essonne","ror":"https://ror.org/00e96v939","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954","https://openalex.org/I88467170"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Lassaad Mchiri","raw_affiliation_strings":["ENSIIE, University of Evry-Val-d\u2019Essonne, \u00c9vry-Courcouronnes, France"],"affiliations":[{"raw_affiliation_string":"ENSIIE, University of Evry-Val-d\u2019Essonne, \u00c9vry-Courcouronnes, France","institution_ids":["https://openalex.org/I88467170","https://openalex.org/I4210097372"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5010661035"],"corresponding_institution_ids":["https://openalex.org/I142899784"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":0.1799,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.46911684,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"2023","issue":null,"first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9994999766349792,"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/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9994999766349792,"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/T10046","display_name":"Stability and Control of Uncertain 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/T10876","display_name":"Fault Detection and Control Systems","score":0.9943000078201294,"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/differentiable-function","display_name":"Differentiable function","score":0.7400752902030945},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.7189820408821106},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7047454714775085},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.6488684415817261},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6322843432426453},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.6266742944717407},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5265410542488098},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.5204042196273804},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39043158292770386},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3783922493457794},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18413814902305603},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.13447102904319763},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.10058265924453735},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05701795220375061},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.047523170709609985}],"concepts":[{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.7400752902030945},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.7189820408821106},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7047454714775085},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.6488684415817261},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6322843432426453},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.6266742944717407},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5265410542488098},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.5204042196273804},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39043158292770386},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3783922493457794},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18413814902305603},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.13447102904319763},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.10058265924453735},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05701795220375061},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.047523170709609985},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"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/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2023/7564084","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2023/7564084","pdf_url":"https://downloads.hindawi.com/journals/complexity/2023/7564084.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:complx:7564084","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/complexity/2023/7564084.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:723eb87f3d424f05874cd402ab1fe92b","is_oa":true,"landing_page_url":"https://doaj.org/article/723eb87f3d424f05874cd402ab1fe92b","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complexity, Vol 2023 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2023/7564084","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2023/7564084","pdf_url":"https://downloads.hindawi.com/journals/complexity/2023/7564084.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2757499628","display_name":null,"funder_award_id":"RSPD2023R683","funder_id":"https://openalex.org/F4320321145","funder_display_name":"King Saud University"}],"funders":[{"id":"https://openalex.org/F4320321145","display_name":"King Saud University","ror":"https://ror.org/02f81g417"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4386518024.pdf","grobid_xml":"https://content.openalex.org/works/W4386518024.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1522228969","https://openalex.org/W1970134289","https://openalex.org/W1982267787","https://openalex.org/W1999913421","https://openalex.org/W2017493230","https://openalex.org/W2027526023","https://openalex.org/W2036826525","https://openalex.org/W2060185628","https://openalex.org/W2080209002","https://openalex.org/W2087276939","https://openalex.org/W2103271720","https://openalex.org/W2162750481","https://openalex.org/W2165626406","https://openalex.org/W2195244501","https://openalex.org/W2276071760","https://openalex.org/W2336049934","https://openalex.org/W2414555924","https://openalex.org/W2592537546","https://openalex.org/W2964207036","https://openalex.org/W3101307053","https://openalex.org/W3113153867","https://openalex.org/W3127551373","https://openalex.org/W3190336611","https://openalex.org/W3211115055","https://openalex.org/W4282838342"],"related_works":["https://openalex.org/W4285277090","https://openalex.org/W4327738859","https://openalex.org/W2348722996","https://openalex.org/W2362838148","https://openalex.org/W2323830966","https://openalex.org/W2334570605","https://openalex.org/W188032563","https://openalex.org/W3181683615","https://openalex.org/W2359279826","https://openalex.org/W4286826125"],"abstract_inverted_index":{"An":[0],"investigation":[1],"of":[2,15,31,66],"the":[3,9,32,48,59,73],"input-to-state":[4,11],"practical":[5,12,61],"stability":[6,13,63],"(ISpS)":[7],"and":[8,29],"integral":[10],"(iISpS)":[14],"nonlinear":[16],"systems":[17,33],"with":[18,51],"time":[19],"delays":[20],"(NSWTDs)":[21],"is":[22],"presented":[23],"in":[24],"this":[25],"paper.":[26],"The":[27],"ISpS":[28],"iISpS":[30],"are":[34],"obtained":[35],"by":[36,71],"using":[37,72],"a":[38,52,57],"continuously":[39],"differentiable":[40],"Lyapunov\u2013Krasovskii":[41],"functional":[42],"(LKF)":[43],"within-definite":[44],"derivative,":[45],"which":[46],"generalizes":[47],"classical":[49],"LKF":[50],"positive":[53],"definite":[54],"derivative.":[55],"As":[56],"result,":[58],"uniform":[60],"asymptotic":[62],"(UPAS)":[64],"criteria":[65],"NSWTD":[67],"were":[68],"also":[69],"given":[70],"proposed":[74],"LKF.":[75]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}