{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T19:22:13Z","timestamp":1754162533463,"version":"3.41.2"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2025,6,6]],"date-time":"2025-06-06T00:00:00Z","timestamp":1749168000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,6,6]],"date-time":"2025-06-06T00:00:00Z","timestamp":1749168000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62073217","62403310","62303309"],"award-info":[{"award-number":["62073217","62403310","62303309"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2025,9]]},"DOI":"10.1007\/s40314-025-03271-2","type":"journal-article","created":{"date-parts":[[2025,6,5]],"date-time":"2025-06-05T22:54:09Z","timestamp":1749164049000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The robust $$H_{\\infty }$$ control of fractional-order systems with distributed delay"],"prefix":"10.1007","volume":"44","author":[{"given":"Yi-Nan","family":"Chen","sequence":"first","affiliation":[]},{"given":"Jun-Guo","family":"Lu","sequence":"additional","affiliation":[]},{"given":"Zhen","family":"Zhu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,6,6]]},"reference":[{"issue":"1","key":"3271_CR1","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1016\/j.jpowsour.2018.08.047","volume":"400","author":"A Allagui","year":"2018","unstructured":"Allagui A, Freeborn TJ, Elwakil AS, Fouda ME, Maundy BJ, Radwan AG, Said Z, Abdelkareem MA (2018) Review of fractional-order electrical characterization of supercapacitors. J Power Sources 400(1):457\u2013467. https:\/\/doi.org\/10.1016\/j.jpowsour.2018.08.047","journal-title":"J Power Sources"},{"issue":"1","key":"3271_CR2","first-page":"116","volume":"4","author":"M ApS","year":"2019","unstructured":"ApS M (2019) Mosek optimization toolbox for matlab. User\u2019s Guide and Reference Manual, Version 4(1):116","journal-title":"User\u2019s Guide and Reference Manual, Version"},{"issue":"3","key":"3271_CR3","doi-asserted-by":"publisher","first-page":"1301","DOI":"10.1109\/TCSII.2023.3323287","volume":"71","author":"Y-N Chen","year":"2024","unstructured":"Chen Y-N, Lu J-G, Jin X-C, Zhu Z (2024) Order-dependent stability and stabilization conditions for fractional-order systems with distributed delays. IEEE Trans Circuits Syst II Exp Briefs 71(3):1301\u20131305. https:\/\/doi.org\/10.1109\/TCSII.2023.3323287","journal-title":"IEEE Trans Circuits Syst II Exp Briefs"},{"issue":"2","key":"3271_CR4","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1007\/s40314-024-02610-z","volume":"43","author":"M Ebrahimi","year":"2024","unstructured":"Ebrahimi M, Alaviyan Shahri ES, Alfi A (2024) A graphical method-based kharitonov theorem for robust stability analysis of incommensurate fractional-order uncertain systems. Computational and Applied Mathematics 43(2):101. https:\/\/doi.org\/10.1007\/s40314-024-02610-z","journal-title":"Computational and Applied Mathematics"},{"issue":"7","key":"3271_CR5","doi-asserted-by":"publisher","first-page":"772","DOI":"10.1016\/j.mechatronics.2013.06.005","volume":"23","author":"C Farges","year":"2013","unstructured":"Farges C, Fadiga L, Sabatier J (2013) $${H}_\\infty $$ analysis and control of commensurate fractional order systems. Mechatronics 23(7):772\u2013780. https:\/\/doi.org\/10.1016\/j.mechatronics.2013.06.005","journal-title":"Mechatronics"},{"key":"3271_CR6","doi-asserted-by":"publisher","unstructured":"Farges C, Moze M, Sabatier J (2009) Pseudo state feedback stabilization of commensurate fractional order systems. In: 2009 European Control Conference (ECC), pp. 3395\u20133400. https:\/\/doi.org\/10.23919\/ECC.2009.7074930. IEEE","DOI":"10.23919\/ECC.2009.7074930"},{"issue":"1","key":"3271_CR7","doi-asserted-by":"publisher","first-page":"84","DOI":"10.3166\/ejc.15.84-94","volume":"15","author":"E Fridman","year":"2009","unstructured":"Fridman E, Tsodik G (2009) $${H}_\\infty $$ control of distributed and discrete delay systems via discretized Lyapunov functional. Eur J Control 15(1):84\u201394. https:\/\/doi.org\/10.3166\/ejc.15.84-94","journal-title":"Eur J Control"},{"key":"3271_CR8","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2020.109011","volume":"117","author":"P Gong","year":"2020","unstructured":"Gong P, Lan W, Han Q-L (2020) Robust adaptive fault-tolerant consensus control for uncertain nonlinear fractional-order multi-agent systems with directed topologies. Automatica 117:109011. https:\/\/doi.org\/10.1016\/j.automatica.2020.109011","journal-title":"Automatica"},{"key":"3271_CR9","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2020.107545","volume":"172","author":"KM Hosny","year":"2020","unstructured":"Hosny KM, Darwish MM, Aboelenen T (2020) Novel fractional-order generic jacobi-fourier moments for image analysis. Signal Process 172:107545. https:\/\/doi.org\/10.1016\/j.sigpro.2020.107545","journal-title":"Signal Process"},{"key":"3271_CR10","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1016\/j.neunet.2020.07.015","volume":"131","author":"C Huang","year":"2020","unstructured":"Huang C, Liu H, Shi X, Chen X, Xiao M, Wang Z, Cao J (2020) Bifurcations in a fractional-order neural network with multiple leakage delays. Neural Netw 131:115\u2013126. https:\/\/doi.org\/10.1016\/j.neunet.2020.07.015","journal-title":"Neural Netw"},{"issue":"3","key":"3271_CR11","doi-asserted-by":"publisher","first-page":"1437","DOI":"10.1109\/TTE.2021.3053063","volume":"7","author":"M Huang","year":"2021","unstructured":"Huang M, Deng Y, Li H, Wang J (2021) Torque ripple suppression of pmsm using fractional-order vector resonant and robust internal model control. IEEE Trans Transp Electrif 7(3):1437\u20131453. https:\/\/doi.org\/10.1109\/TTE.2021.3053063","journal-title":"IEEE Trans Transp Electrif"},{"issue":"5","key":"3271_CR12","doi-asserted-by":"publisher","first-page":"801","DOI":"10.3390\/math8050801","volume":"8","author":"U Humphries","year":"2020","unstructured":"Humphries U, Rajchakit G, Kaewmesri P, Chanthorn P, Sriraman R, Samidurai R, Lim CP (2020) Global stability analysis of fractional-order quaternion-valued bidirectional associative memory neural networks. Mathematics 8(5):801. https:\/\/doi.org\/10.3390\/math8050801","journal-title":"Mathematics"},{"issue":"3","key":"3271_CR13","doi-asserted-by":"publisher","first-page":"356","DOI":"10.1109\/9.50357","volume":"35","author":"PP Khargonekar","year":"1990","unstructured":"Khargonekar PP, Petersen IR, Zhou K (1990) Robust stabilization of uncertain linear systems: quadratic stabilizability and $${H}_\\infty $$ control theory. IEEE Trans Automat Contr 35(3):356\u2013361. https:\/\/doi.org\/10.1109\/9.50357","journal-title":"IEEE Trans Automat Contr"},{"key":"3271_CR14","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2022.112133","volume":"159","author":"X Li","year":"2022","unstructured":"Li X, Mou J, Banerjee S, Wang Z, Cao Y (2022) Design and DSP implementation of a fractional-order detuned laser hyperchaotic circuit with applications in image encryption. Chaos Solitons Fractals 159:112133. https:\/\/doi.org\/10.1016\/j.chaos.2022.112133","journal-title":"Chaos Solitons Fractals"},{"issue":"3","key":"3271_CR15","doi-asserted-by":"publisher","first-page":"164","DOI":"10.3390\/fractalfract6030164","volume":"6","author":"B Li","year":"2022","unstructured":"Li B, Zhao X, Liu Y, Zhao X (2022) Robust $${H}_\\infty $$ control of fractional-order switched systems with order $$0< \\alpha < 1$$ and uncertainty. Fractal Fract 6(3):164. https:\/\/doi.org\/10.3390\/fractalfract6030164","journal-title":"Fractal Fract"},{"key":"3271_CR16","doi-asserted-by":"publisher","unstructured":"Liu G, Luo C, Luo X, Zhao W (2016) H infinity state estimation for neutral-type neural networks with continuously distributed delays. In: 2016 12th World Congress on Intelligent Control and Automation (WCICA), pp. 2098\u20132102. https:\/\/doi.org\/10.1109\/WCICA.2016.7578805. IEEE","DOI":"10.1109\/WCICA.2016.7578805"},{"issue":"2","key":"3271_CR17","doi-asserted-by":"publisher","first-page":"698","DOI":"10.1109\/TNSE.2022.3217618","volume":"10","author":"G Narayanan","year":"2023","unstructured":"Narayanan G, Ali MS, Zhu Q, Priya B, Thakur GK (2023) Fuzzy observer-based consensus tracking control for fractional-order multi-agent systems under cyber-attacks and its application to electronic circuits. IEEE Trans Network Sci Eng 10(2):698\u2013708. https:\/\/doi.org\/10.1109\/TNSE.2022.3217618","journal-title":"IEEE Trans Network Sci Eng"},{"key":"3271_CR18","volume-title":"Modern Control Engineering","author":"K Ogata","year":"2010","unstructured":"Ogata K (2010) Modern Control Engineering. Prentice Hall, New Jersey"},{"key":"3271_CR19","doi-asserted-by":"publisher","unstructured":"Pan W (2010) Delay-dependent robust $${H}_\\infty $$ control for uncertain singular systems with discrete and distributed delays. In: 2010 Chinese Control and Decision Conference, pp. 555\u2013560. https:\/\/doi.org\/10.1109\/CCDC.2010.5498987. IEEE","DOI":"10.1109\/CCDC.2010.5498987"},{"key":"3271_CR20","volume-title":"Fractional Differential Equations","author":"I Podlubny","year":"1999","unstructured":"Podlubny I (1999) Fractional Differential Equations. Academic Press, New York"},{"issue":"8","key":"3271_CR21","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-Liouville sense fractional order memristive BAM neural networks with mixed delays. Mathematics 7(8):759. https:\/\/doi.org\/10.3390\/math7080759","journal-title":"Mathematics"},{"issue":"3","key":"3271_CR22","doi-asserted-by":"publisher","first-page":"422","DOI":"10.3390\/math8030422","volume":"8","author":"G Rajchakit","year":"2020","unstructured":"Rajchakit G, Chanthorn P, Kaewmesri P, Sriraman R, Lim CP (2020) Global Mittag-Leffler stability and stabilization analysis of fractional-order quaternion-valued memristive neural networks. Mathematics 8(3):422. https:\/\/doi.org\/10.3390\/math8030422","journal-title":"Mathematics"},{"key":"3271_CR23","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. https:\/\/doi.org\/10.1016\/j.neucom.2020.07.036","journal-title":"Neurocomputing"},{"key":"3271_CR24","doi-asserted-by":"publisher","unstructured":"Saravanakumar R, Ali MS (2014) H-infinity state estimation control of neural networks with distributed time-varying delays. In: 2014 International Conference on Soft Computing and Machine Intelligence, pp. 11\u201314. https:\/\/doi.org\/10.1109\/ISCMI.2014.36. IEEE","DOI":"10.1109\/ISCMI.2014.36"},{"issue":"4","key":"3271_CR25","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 Equ Dyn Syst 29(4):825\u2013839. https:\/\/doi.org\/10.1007\/s12591-020-00559-z","journal-title":"Differ Equ Dyn Syst"},{"issue":"3","key":"3271_CR26","doi-asserted-by":"publisher","first-page":"1813","DOI":"10.1007\/s12190-024-02031-5","volume":"70","author":"NH Sau","year":"2024","unstructured":"Sau NH, Binh TN, Thanh NT, Thuan MV (2024) Event-triggered $${H}_\\infty $$ controller design for uncertain fractional-order systems with time-varying delays. J Appl Math Comput 70(3):1813\u20131835. https:\/\/doi.org\/10.1007\/s12190-024-02031-5","journal-title":"J Appl Math Comput"},{"key":"3271_CR27","doi-asserted-by":"publisher","unstructured":"Wang J-L, Wang C-H (2004) Delay-dependent $${H}_\\infty $$ control for LPV systems with mixed time-varying delays. In: 2004 International Conference on Machine Learning and Cybernetics, pp. 626\u2013631. https:\/\/doi.org\/10.1109\/ICMLC.2004.1380767","DOI":"10.1109\/ICMLC.2004.1380767"},{"issue":"1","key":"3271_CR28","doi-asserted-by":"publisher","first-page":"206","DOI":"10.1109\/TNNLS.2015.2506738","volume":"28","author":"A Wu","year":"2015","unstructured":"Wu A, Zeng Z (2015) Global mittag-leffler stabilization of fractional-order memristive neural networks. IEEE Trans Neural Netw Learn Syst 28(1):206\u2013217. https:\/\/doi.org\/10.1109\/TNNLS.2015.2506738","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"issue":"12","key":"3271_CR29","doi-asserted-by":"publisher","first-page":"1930","DOI":"10.1109\/9.975483","volume":"46","author":"L Xie","year":"2001","unstructured":"Xie L, Fridman E, Shaked U (2001) Robust $${H}_\\infty $$ control of distributed delay systems with application to combustion control. IEEE Trans Autom Control 46(12):1930\u20131935. https:\/\/doi.org\/10.1109\/9.975483","journal-title":"IEEE Trans Autom Control"},{"key":"3271_CR30","doi-asserted-by":"publisher","first-page":"681","DOI":"10.1016\/j.neucom.2021.11.079","volume":"488","author":"C Xu","year":"2022","unstructured":"Xu C, Zhang W, Liu Z, Yao L (2022) Delay-induced periodic oscillation for fractional-order neural networks with mixed delays. Neurocomputing 488:681\u2013693. https:\/\/doi.org\/10.1016\/j.neucom.2021.11.079","journal-title":"Neurocomputing"},{"key":"3271_CR31","doi-asserted-by":"publisher","DOI":"10.1016\/j.optlaseng.2020.106031","volume":"129","author":"F Yang","year":"2020","unstructured":"Yang F, Mou J, Ma C, Cao Y (2020) Dynamic analysis of an improper fractional-order laser chaotic system and its image encryption application. Opt Lasers Eng 129:106031. https:\/\/doi.org\/10.1016\/j.optlaseng.2020.106031","journal-title":"Opt Lasers Eng"},{"issue":"7","key":"3271_CR32","doi-asserted-by":"publisher","first-page":"3701","DOI":"10.1016\/j.jfranklin.2021.03.006","volume":"358","author":"Z Yang","year":"2021","unstructured":"Yang Z, Ding Q, Sun X, Zhu H, Lu C (2021) Fractional-order sliding mode control for a bearingless induction motor based on improved load torque observer. J Franklin Inst 358(7):3701\u20133725. https:\/\/doi.org\/10.1016\/j.jfranklin.2021.03.006","journal-title":"J Franklin Inst"},{"issue":"1","key":"3271_CR33","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1364\/OE.444739","volume":"30","author":"X Zhang","year":"2021","unstructured":"Zhang X, Li R, Hong J, Zhou X, Xin N, Li Q (2021) Image-enhanced single-pixel imaging using fractional calculus. Opt Express 30(1):81\u201391. https:\/\/doi.org\/10.1364\/OE.444739","journal-title":"Opt Express"},{"issue":"8","key":"3271_CR34","doi-asserted-by":"publisher","first-page":"5056","DOI":"10.1109\/TSMC.2021.3113673","volume":"52","author":"Q-H Zhang","year":"2022","unstructured":"Zhang Q-H, Lu J-G, Xu J, Chen Y-Q (2022) Solution analysis and novel admissibility conditions of SFOSs: the $$1< \\alpha < 2$$ case. IEEE Trans Syst Man Cybern: Syst 52(8):5056\u20135067. https:\/\/doi.org\/10.1109\/TSMC.2021.3113673","journal-title":"IEEE Trans Syst Man Cybern: Syst"},{"issue":"6","key":"3271_CR35","doi-asserted-by":"publisher","first-page":"8086","DOI":"10.1109\/TNNLS.2022.3224393","volume":"35","author":"X Zhang","year":"2024","unstructured":"Zhang X, Li C, Li H, Xu J (2024) Synchronization of neural networks involving distributed-delay coupling: A distributed-delay differential inequalities approach. IEEE Trans Neural Netw Learn Syst 35(6):8086\u20138096. https:\/\/doi.org\/10.1109\/TNNLS.2022.3224393","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"3271_CR36","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1016\/j.neucom.2018.08.031","volume":"321","author":"Z Zhao","year":"2018","unstructured":"Zhao Z, Wang Z, Zou L, Liu H (2018) Finite-horizon $${H}_\\infty $$ state estimation for artificial neural networks with component-based distributed delays and stochastic protocol. Neurocomputing 321:169\u2013177. https:\/\/doi.org\/10.1016\/j.neucom.2018.08.031","journal-title":"Neurocomputing"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-025-03271-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-025-03271-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-025-03271-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T08:07:21Z","timestamp":1753862841000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-025-03271-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,6]]},"references-count":36,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2025,9]]}},"alternative-id":["3271"],"URL":"https:\/\/doi.org\/10.1007\/s40314-025-03271-2","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"type":"print","value":"2238-3603"},{"type":"electronic","value":"1807-0302"}],"subject":[],"published":{"date-parts":[[2025,6,6]]},"assertion":[{"value":"22 September 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 April 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 May 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 June 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflicts of Interest"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Materials Availability"}},{"value":"Not applicable.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Code Availability"}}],"article-number":"309"}}