{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T01:02:28Z","timestamp":1767142948963,"version":"build-2238731810"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2025,3,18]],"date-time":"2025-03-18T00:00:00Z","timestamp":1742256000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,3,18]],"date-time":"2025-03-18T00:00:00Z","timestamp":1742256000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2025,6]]},"DOI":"10.1007\/s40314-025-03162-6","type":"journal-article","created":{"date-parts":[[2025,3,17]],"date-time":"2025-03-17T20:52:01Z","timestamp":1742244721000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["H$$_\\infty $$ observer-based control for fuzzy Hadamard fractional-order systems"],"prefix":"10.1007","volume":"44","author":[{"given":"Mohamed","family":"Rhaima","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hamdi","family":"Gassara","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lassaad","family":"Mchiri","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7564-3620","authenticated-orcid":false,"given":"Ahmed","family":"El Hajjaji","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abdellatif","family":"Ben Makhlouf","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,3,18]]},"reference":[{"key":"3162_CR1","volume-title":"Hadamard-Type Fractional Differential Equations","author":"B Ahmad","year":"2017","unstructured":"Ahmad B, Alsaedi A, Ntouyas SK, Tariboon J (2017) Hadamard-Type Fractional Differential Equations. Inclusions and Inequalities, Springer, Switzerland"},{"key":"3162_CR2","doi-asserted-by":"publisher","first-page":"214","DOI":"10.1007\/s40314-021-01595-3","volume":"40","author":"M Bohner","year":"2021","unstructured":"Bohner M, Tun\u00e7 O, Tun\u00e7 C (2021) Qualitative analysis of caputo fractional integro-differential equations with constant delays. Comput Appl Math 40:214","journal-title":"Comput Appl Math"},{"key":"3162_CR3","volume":"453","author":"Y Di","year":"2023","unstructured":"Di Y, Zhang JX, Zhang X (2023) Robust stabilization of descriptor fractional-order interval systems with uncertain derivative matrices. Appl Math Comput 453:128076","journal-title":"Appl Math Comput"},{"key":"3162_CR4","doi-asserted-by":"publisher","first-page":"577","DOI":"10.3390\/fractalfract7080577","volume":"7","author":"Y Di","year":"2023","unstructured":"Di Y, Zhang JX, Zhang X (2023) Alternate Admissibility LMI Criteria for Descriptor Fractional Order Systems with $$0<\\alpha <2$$. Fractal Fract 7:577","journal-title":"Fractal Fract"},{"issue":"14","key":"3162_CR5","doi-asserted-by":"publisher","first-page":"9423","DOI":"10.1016\/j.jfranklin.2020.07.017","volume":"357","author":"T Feng","year":"2020","unstructured":"Feng T, Wang Y-E, Liu L, Wu B (2020) Observer-based event-triggered control for uncertain fractional-order systems. J Franklin Inst 357(14):9423\u20139441","journal-title":"J Franklin Inst"},{"issue":"6","key":"3162_CR6","doi-asserted-by":"publisher","first-page":"1783","DOI":"10.1007\/s40815-024-01703-5","volume":"26","author":"Y Hao","year":"2024","unstructured":"Hao Y, Liu H, Fang Z (2024) Observer-based adaptive control for uncertain fractional-order T-S fuzzy Systems with output disturbances. Int J Fuzzy Syst 26(6):1783\u20131801","journal-title":"Int J Fuzzy Syst"},{"key":"3162_CR7","doi-asserted-by":"publisher","unstructured":"He BB, Zhou HC (2022) Caputo-Hadamard fractional Halanay inequality, Applied Mathematics Letters, 125, https:\/\/doi.org\/10.1016\/j.aml.2021.107723","DOI":"10.1016\/j.aml.2021.107723"},{"key":"3162_CR8","doi-asserted-by":"publisher","first-page":"2420","DOI":"10.1007\/s13540-022-00106-3","volume":"25","author":"BB He","year":"2022","unstructured":"He BB, Zhou HC, Kou CH (2022) Stability analysis of Hadamard and Caputo-Hadamard fractional nonlinear systems without and with delay. Fract Calc Appl Anal 25:2420\u20132445","journal-title":"Fract Calc Appl Anal"},{"key":"3162_CR9","doi-asserted-by":"publisher","first-page":"5142","DOI":"10.1007\/s00034-023-02358-7","volume":"42","author":"NTT Huyen","year":"2023","unstructured":"Huyen NTT, Thanh NT, Sau NH, Binh TN, Thuan MV (2023) Mixed $$H_\\infty $$ and passivity performance for delayed conformable fractional-order neural networks. Circ Syst Signal Process 42:5142\u20135160","journal-title":"Circ Syst Signal Process"},{"key":"3162_CR10","doi-asserted-by":"crossref","unstructured":"Jmal A, Naifar O, Ben Makhlouf A, Derbel N, Hammami MA (2018) Sensor fault estimation for fractional-order descriptor one-sided Lipschitz systems , Nonlinear dynamics, 91:1713-1722","DOI":"10.1007\/s11071-017-3976-1"},{"key":"3162_CR11","volume-title":"Theory and applications of fractional differential equations","author":"AA Kilbas","year":"2006","unstructured":"Kilbas AA, Srivastava HM, Trujillo JJ (2006) Theory and applications of fractional differential equations. Elsevier, Amsterdam"},{"issue":"2","key":"3162_CR12","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1115\/1.3167616","volume":"51","author":"R Koeller","year":"1984","unstructured":"Koeller R (1984) Applications of fractional calculus to the theory of viscoelasticity. ASME J Appl Mech 51(2):299\u2013307","journal-title":"ASME J Appl Mech"},{"key":"3162_CR13","doi-asserted-by":"publisher","first-page":"3749","DOI":"10.1007\/s11071-021-07138-z","volume":"107","author":"L Ma","year":"2022","unstructured":"Ma L, Wu B (2022) Finite-time stability of Hadamard fractional differential equations in weighted Banach spaces. Nonlinear Dyn 107:3749\u20133766","journal-title":"Nonlinear Dyn"},{"issue":"2","key":"3162_CR14","doi-asserted-by":"publisher","first-page":"443","DOI":"10.1080\/00207721.2022.2122900","volume":"54","author":"S Maalej","year":"2023","unstructured":"Maalej S, Kruszewski A (2023) Stability and performances synthesis of a class of Takagi\u2013Sugeno systems with unmeasured premises: restricted-model-based approach. Int J Syst Sci 54(2):443\u2013461","journal-title":"Int J Syst Sci"},{"key":"3162_CR15","doi-asserted-by":"crossref","unstructured":"Monje CA, Chen Y, Vinagre BM, Xue D, Feliu-Batlle V (2010) Fractional-Order Systems and Controls: Fundamentals and Applications, Springer, ISBN 9781849963350","DOI":"10.1007\/978-1-84996-335-0"},{"key":"3162_CR16","doi-asserted-by":"publisher","first-page":"42697","DOI":"10.1109\/ACCESS.2021.3060093","volume":"9","author":"R Peng","year":"2021","unstructured":"Peng R, Jiang C, Guo R (2021) Stabilization of a class of fractional order systems with both uncertainty and disturbance. IEEE access 9:42697\u201342706","journal-title":"IEEE access"},{"key":"3162_CR17","volume-title":"Fractional Differential Equations","author":"I Podlubny","year":"1999","unstructured":"Podlubny I (1999) Fractional Differential Equations. Academic Press, San Diego"},{"key":"3162_CR18","doi-asserted-by":"publisher","first-page":"759","DOI":"10.3390\/math7080759","volume":"7","author":"G Rajchakit","year":"2019","unstructured":"Rajchakit G, Pratap A, Raja R, Cao J, Alzabut J, Huang C (2019) Hybrid control scheme for projective lag synchronization of Riemann\u2013Liouville sense fractional order memristive BAM neural networks with mixed delays. Mathematics 7:759","journal-title":"Mathematics"},{"key":"3162_CR19","doi-asserted-by":"publisher","first-page":"290","DOI":"10.1016\/j.neucom.2020.07.036","volume":"417","author":"G Rajchakit","year":"2020","unstructured":"Rajchakit G, Chanthorn P, Niezabitowski M, Raja R, Baleanu D, Pratap A (2020) Impulsive effects on stability and passivity analysis of memristor-based fractional-order competitive neural networks. Neurocomputing 417:290\u2013301","journal-title":"Neurocomputing"},{"key":"3162_CR20","doi-asserted-by":"publisher","first-page":"825","DOI":"10.1007\/s12591-020-00559-z","volume":"29","author":"NH Sau","year":"2021","unstructured":"Sau NH, Hong DT, Huyen NTT, Huong BV, Thuan MV (2021) Delay-dependent and order-dependent $$H_\\infty $$ control for fractional-order neural networks with time-varying delay. Differ Eqs Dyn Syst 29:825\u2013839","journal-title":"Differ Eqs Dyn Syst"},{"issue":"1","key":"3162_CR21","doi-asserted-by":"publisher","first-page":"116","DOI":"10.1109\/TSMC.1985.6313399","volume":"15","author":"T Takagi","year":"1985","unstructured":"Takagi T, Sugeno M (1985) Fuzzy identification of systems and its applications to modelling and control. IEEE Trans Syst Man Cybernet 15(1):116\u2013132","journal-title":"IEEE Trans Syst Man Cybernet"},{"key":"3162_CR22","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1016\/j.nahs.2019.05.002","volume":"34","author":"Y Tan","year":"2019","unstructured":"Tan Y, Xiong M, Du D, Fei S (2019) Observer-based robust control for fractional-order nonlinear uncertain systems with input saturation and measurement quantization. Nonlinear Anal Hybrid Syst 34:45\u201357","journal-title":"Nonlinear Anal Hybrid Syst"},{"key":"3162_CR23","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1007\/s40314-020-1069-0","volume":"39","author":"MV Thuan","year":"2020","unstructured":"Thuan MV, Sau NH, Huyen NTT (2020) Finite-time $$H_\\infty $$ control of uncertain fractional-order neural networks. Comput Appl Math 39:59","journal-title":"Comput Appl Math"},{"key":"3162_CR24","doi-asserted-by":"publisher","first-page":"72","DOI":"10.1016\/j.isatra.2016.06.014","volume":"65","author":"B Wang","year":"2016","unstructured":"Wang B, Xue J, Wu F, Zhu D (2016) Robust Takagi-Sugeno fuzzy control for fractional order hydro-turbine governing system. ISA Trans 65:72\u201380","journal-title":"ISA Trans"},{"key":"3162_CR25","doi-asserted-by":"publisher","first-page":"6538","DOI":"10.1016\/j.jfranklin.2018.12.033","volume":"356","author":"G Wang","year":"2019","unstructured":"Wang G, Pei K, Chen YQ (2019) Stability analysis of nonlinear Hadamard fractional differential system. J Franklin Inst 356:6538\u20136546","journal-title":"J Franklin Inst"},{"key":"3162_CR26","doi-asserted-by":"publisher","first-page":"116","DOI":"10.1007\/s40314-023-02257-2","volume":"42","author":"J Xiao-Chuang","year":"2023","unstructured":"Xiao-Chuang J, Jun-Guo L, Qing-Hao Z (2023) Delay-dependent and order-dependent asymptotic stability conditions for Riemann\u2013Liouville fractional-order systems with time delays. Comput Appl Math 42:116","journal-title":"Comput Appl Math"},{"key":"3162_CR27","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1007\/s40314-022-02122-8","volume":"42","author":"Y Zhang","year":"2022","unstructured":"Zhang Y, Li J, Zhu S, Wang H (2022) Asymptotical stability and synchronization of Riemann\u2013Liouville fractional delayed neural networks. Comput Appl Mathe 42:20","journal-title":"Comput Appl Mathe"},{"key":"3162_CR28","doi-asserted-by":"publisher","first-page":"344","DOI":"10.1007\/s40314-022-02062-3","volume":"41","author":"H Zhang","year":"2022","unstructured":"Zhang H, Wang C, Zhang W, Zhang H (2022) Mittag-Leffler stability and synchronization for FOQVFNNs including proportional delay and Caputo derivative via fractional differential inequality approach. Comput Appl Math 41:344","journal-title":"Comput Appl Math"},{"key":"3162_CR29","volume":"434","author":"X Zhang","year":"2022","unstructured":"Zhang X, Chen S, Zhang JX (2022) Adaptive sliding mode consensus control based on neural network for singular fractional order multi-agent systems. Appl Math Comput 434:127442","journal-title":"Appl Math Comput"},{"key":"3162_CR30","doi-asserted-by":"crossref","unstructured":"Zhang X, Wang Z (2020) Stabilisation of Takagi-Sugeno fuzzy singular fractional-order systems subject to actuator saturation, Int J Syst Sci 51(16)","DOI":"10.1080\/00207721.2020.1809749"}],"updated-by":[{"DOI":"10.1007\/s40314-025-03193-z","type":"correction","label":"Correction","source":"publisher","updated":{"date-parts":[[2025,4,24]],"date-time":"2025-04-24T00:00:00Z","timestamp":1745452800000}}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-025-03162-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-025-03162-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-025-03162-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,24]],"date-time":"2025-04-24T03:27:49Z","timestamp":1745465269000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-025-03162-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,18]]},"references-count":30,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,6]]}},"alternative-id":["3162"],"URL":"https:\/\/doi.org\/10.1007\/s40314-025-03162-6","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,18]]},"assertion":[{"value":"18 March 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 November 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 February 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 March 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 April 2025","order":5,"name":"change_date","label":"Change Date","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Correction","order":6,"name":"change_type","label":"Change Type","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"A Correction to this paper has been published:","order":7,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"https:\/\/doi.org\/10.1007\/s40314-025-03193-z","URL":"https:\/\/doi.org\/10.1007\/s40314-025-03193-z","order":8,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no Conflict of interest to declare. All co-authors have seen and agree with the contents of the manuscript. We certify that the submission is original work and is not under review at any other publication.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"194"}}