{"id":"https://openalex.org/W7204528516","doi":"https://doi.org/10.1016/b978-0-44-345038-9.00008-5","title":"Stability of commensurate fractional discrete time systems","display_name":"Stability of commensurate fractional discrete time systems","publication_year":2026,"publication_date":"2026-08-28","ids":{"openalex":"https://openalex.org/W7204528516","doi":"https://doi.org/10.1016/b978-0-44-345038-9.00008-5"},"language":"en","primary_location":{"id":"doi:10.1016/b978-0-44-345038-9.00008-5","doi":"https://doi.org/10.1016/b978-0-44-345038-9.00008-5","is_oa":false,"landing_page_url":"https://doi.org/10.1016/b978-0-44-345038-9.00008-5","pdf_url":null,"source":{"id":"https://openalex.org/S4306463230","display_name":"Elsevier eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Dynamics and Control of Fractional Discrete Time Systems","raw_type":"book-chapter"},"volume":{"id":"https://openalex.org/W7204558377","display_name":"Advances in Dynamics and Control of Fractional Discrete Time Systems"},"type":"book-chapter","is_traditional":true,"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/A5025265960","display_name":"Noureddine Djenina","orcid":"https://orcid.org/0000-0003-3492-1249","observed_orcids":["https://orcid.org/0000-0003-3492-1249","https://orcid.org/0009-0003-1086-9930"]},"institutions":[{"id":"https://openalex.org/I4387153399","display_name":"University of Batna 2","ror":"https://ror.org/02yvp6477","country_code":"DZ","type":"education","lineage":["https://openalex.org/I4387153399"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Noureddine Djenina","raw_affiliation_strings":["Institute of Hygiene and Safety, University of Mustapha Ben Boulaid Batna 2, Batna, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Hygiene and Safety, University of Mustapha Ben Boulaid Batna 2, Batna, Algeria","institution_ids":["https://openalex.org/I4387153399"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027644473","display_name":"Adel Ouannas","orcid":"https://orcid.org/0000-0001-9611-2047","observed_orcids":["https://orcid.org/0000-0001-9611-2047","https://orcid.org/0000-0002-0298-1194"]},"institutions":[{"id":"https://openalex.org/I3132180716","display_name":"Larbi Ben M'hidi University of Oum El Bouaghi","ror":"https://ror.org/0034tbg85","country_code":"DZ","type":"education","lineage":["https://openalex.org/I3132180716"]},{"id":"https://openalex.org/I4210151290","display_name":"Islamic University of Madinah","ror":"https://ror.org/03rcp1y74","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210151290"]}],"countries":["DZ","SA"],"is_corresponding":false,"raw_author_name":"Adel Ouannas","raw_affiliation_strings":["Department of Mathematics and Computer Science, Larbi Ben M'hidi University, Oum El Bouaghi, Algeria","Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Larbi Ben M'hidi University, Oum El Bouaghi, Algeria","institution_ids":["https://openalex.org/I3132180716"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, Saudi Arabia","institution_ids":["https://openalex.org/I4210151290"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010661035","display_name":"Abdellatif Ben Makhlouf","orcid":"https://orcid.org/0000-0001-7142-7026","observed_orcids":["https://orcid.org/0000-0001-7142-7026","https://orcid.org/0009-0000-2719-5985","https://orcid.org/0000-0003-1534-4271","https://orcid.org/0000-0001-8774-3525","https://orcid.org/0000-0002-4955-0842"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Abdellatif Ben Makhlouf","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5148508207","display_name":"Omar Naifar","orcid":"https://orcid.org/0000-0002-3426-6435","observed_orcids":["https://orcid.org/0000-0002-3426-6435","https://orcid.org/0000-0002-7929-5811"]},"institutions":[{"id":"https://openalex.org/I55167344","display_name":"University of Kairouan","ror":"https://ror.org/024mpte60","country_code":"TN","type":"education","lineage":["https://openalex.org/I55167344"]}],"countries":["TN"],"is_corresponding":false,"raw_author_name":"Omar Naifar","raw_affiliation_strings":["Higher Institute of Applied Sciences and Technology of Kairouan, University of Kairouan, Kairouan, Tunisia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Higher Institute of Applied Sciences and Technology of Kairouan, University of Kairouan, Kairouan, Tunisia","institution_ids":["https://openalex.org/I55167344"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"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":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"43","last_page":"73"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11081","display_name":"Advanced Control Systems Design","score":0.7519999742507935,"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/T11081","display_name":"Advanced Control Systems Design","score":0.7519999742507935,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.18790000677108765,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.05000000074505806,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/stability-analysis","display_name":"stability analysis","score":0.765999972820282},{"id":"https://openalex.org/keywords/discrete-time-systems","display_name":"discrete-time systems","score":0.824999988079071},{"id":"https://openalex.org/keywords/fractional-order-systems","display_name":"fractional-order systems","score":0.8939999938011169},{"id":"https://openalex.org/keywords/lyapunov-stability","display_name":"Lyapunov stability","score":0.9610000252723694},{"id":"https://openalex.org/keywords/asymptotic-stability","display_name":"asymptotic stability","score":0.9869999885559082},{"id":"https://openalex.org/keywords/global-stability","display_name":"global stability","score":1.0},{"id":"https://openalex.org/keywords/nonlinear-systems","display_name":"nonlinear systems","score":0.7160000205039978},{"id":"https://openalex.org/keywords/linearization","display_name":"linearization","score":0.7829999923706055},{"id":"https://openalex.org/keywords/lyapunov-direct-method","display_name":"Lyapunov direct method","score":0.9700000286102295}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6854000091552734},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6258999705314636},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5945000052452087},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.5389000177383423},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5291000008583069},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4853000044822693},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.46950000524520874},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.46070000529289246},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.4546000063419342},{"id":"https://openalex.org/C54207081","wikidata":"https://www.wikidata.org/wiki/Q937750","display_name":"Nabla symbol","level":3,"score":0.41200000047683716},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.3659999966621399},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.35429999232292175},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3449000120162964},{"id":"https://openalex.org/C2776829284","wikidata":"https://www.wikidata.org/wiki/Q1341651","display_name":"Lyapunov stability","level":3,"score":0.3357999920845032},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.33180001378059387},{"id":"https://openalex.org/C96314035","wikidata":"https://www.wikidata.org/wiki/Q5282062","display_name":"Discrete system","level":2,"score":0.30809998512268066},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.3077000081539154},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.2921000123023987},{"id":"https://openalex.org/C143170015","wikidata":"https://www.wikidata.org/wiki/Q17007850","display_name":"Stability conditions","level":3,"score":0.28850001096725464},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2671999931335449},{"id":"https://openalex.org/C41949839","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theory","level":3,"score":0.25920000672340393}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/b978-0-44-345038-9.00008-5","doi":"https://doi.org/10.1016/b978-0-44-345038-9.00008-5","is_oa":false,"landing_page_url":"https://doi.org/10.1016/b978-0-44-345038-9.00008-5","pdf_url":null,"source":{"id":"https://openalex.org/S4306463230","display_name":"Elsevier eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Dynamics and Control of Fractional Discrete Time Systems","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":124,"referenced_works":["https://openalex.org/W807515142","https://openalex.org/W1908664704","https://openalex.org/W1990990035","https://openalex.org/W1994115058","https://openalex.org/W2274596104","https://openalex.org/W2411043875","https://openalex.org/W2495165290","https://openalex.org/W2511242712","https://openalex.org/W2567237076","https://openalex.org/W2577305827","https://openalex.org/W2590196486","https://openalex.org/W2623930225","https://openalex.org/W2767717692","https://openalex.org/W2800167209","https://openalex.org/W2883960285","https://openalex.org/W2888893773","https://openalex.org/W2889823359","https://openalex.org/W2889881165","https://openalex.org/W2890658529","https://openalex.org/W2892457839","https://openalex.org/W2904125316","https://openalex.org/W2905113890","https://openalex.org/W2912385041","https://openalex.org/W2915398395","https://openalex.org/W2922403648","https://openalex.org/W2923223771","https://openalex.org/W2930398221","https://openalex.org/W2932777356","https://openalex.org/W2945029848","https://openalex.org/W2946911774","https://openalex.org/W2954522472","https://openalex.org/W2977209716","https://openalex.org/W2999899931","https://openalex.org/W3013342027","https://openalex.org/W3014639127","https://openalex.org/W3015780933","https://openalex.org/W3021086917","https://openalex.org/W3021550721","https://openalex.org/W3024763774","https://openalex.org/W3030637055","https://openalex.org/W3034099877","https://openalex.org/W3080492959","https://openalex.org/W3089285989","https://openalex.org/W3092011670","https://openalex.org/W3092470496","https://openalex.org/W3093078194","https://openalex.org/W3095214280","https://openalex.org/W3095875068","https://openalex.org/W3103642871","https://openalex.org/W3109159933","https://openalex.org/W3111787112","https://openalex.org/W3118752909","https://openalex.org/W3148737134","https://openalex.org/W3165156628","https://openalex.org/W3168928645","https://openalex.org/W3169638822","https://openalex.org/W3174477285","https://openalex.org/W3181152850","https://openalex.org/W3183095410","https://openalex.org/W3209680301","https://openalex.org/W3213506382","https://openalex.org/W4210382181","https://openalex.org/W4210425277","https://openalex.org/W4210666921","https://openalex.org/W4210932665","https://openalex.org/W4213146444","https://openalex.org/W4213416137","https://openalex.org/W4220943556","https://openalex.org/W4226158921","https://openalex.org/W4283580680","https://openalex.org/W4284974469","https://openalex.org/W4291493428","https://openalex.org/W4291717616","https://openalex.org/W4292962223","https://openalex.org/W4293090900","https://openalex.org/W4294845578","https://openalex.org/W4297236549","https://openalex.org/W4303946440","https://openalex.org/W4309348246","https://openalex.org/W4309821992","https://openalex.org/W4310034915","https://openalex.org/W4313528227","https://openalex.org/W4313583190","https://openalex.org/W4317743338","https://openalex.org/W4318208685","https://openalex.org/W4318214870","https://openalex.org/W4365816379","https://openalex.org/W4376870739","https://openalex.org/W4378377574","https://openalex.org/W4379793314","https://openalex.org/W4380875019","https://openalex.org/W4381618516","https://openalex.org/W4383068603","https://openalex.org/W4384934702","https://openalex.org/W4384935578","https://openalex.org/W4385368219","https://openalex.org/W4385423788","https://openalex.org/W4385732675","https://openalex.org/W4386074059","https://openalex.org/W4386351980","https://openalex.org/W4387251867","https://openalex.org/W4387264808","https://openalex.org/W4387373185","https://openalex.org/W4387450521","https://openalex.org/W4387667593","https://openalex.org/W4387743830","https://openalex.org/W4388830739","https://openalex.org/W4388945375","https://openalex.org/W4392727936","https://openalex.org/W4394688174","https://openalex.org/W4399124780","https://openalex.org/W4400248198","https://openalex.org/W4400280166","https://openalex.org/W4401444490","https://openalex.org/W4401756577","https://openalex.org/W4401947510","https://openalex.org/W4401947739","https://openalex.org/W4403106871","https://openalex.org/W4403939500","https://openalex.org/W4405968483","https://openalex.org/W4406330516","https://openalex.org/W4406599502","https://openalex.org/W4406608682","https://openalex.org/W4407972872"],"related_works":["https://openalex.org/W7204561080","https://openalex.org/W114976905","https://openalex.org/W7204586709","https://openalex.org/W7204598985","https://openalex.org/W2767030519","https://openalex.org/W2571497543","https://openalex.org/W2101727141","https://openalex.org/W4411048512","https://openalex.org/W2567584285","https://openalex.org/W7204534539"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2026-08-29T00:00:00"}
