{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T16:49:31Z","timestamp":1784134171543,"version":"3.55.0"},"reference-count":46,"publisher":"Springer Science and Business Media LLC","issue":"9","license":[{"start":{"date-parts":[[2025,4,2]],"date-time":"2025-04-02T00:00:00Z","timestamp":1743552000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,4,2]],"date-time":"2025-04-02T00:00:00Z","timestamp":1743552000000},"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":["Sci. China Inf. Sci."],"published-print":{"date-parts":[[2025,9]]},"DOI":"10.1007\/s11432-024-4226-x","type":"journal-article","created":{"date-parts":[[2025,4,5]],"date-time":"2025-04-05T23:20:22Z","timestamp":1743895222000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Finite-time synchronization control for a class of delayed neural networks: an improved two-step control method"],"prefix":"10.1007","volume":"68","author":[{"given":"Yue","family":"Chen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Song","family":"Zhu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mouquan","family":"Shen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoyang","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shiping","family":"Wen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,4,2]]},"reference":[{"key":"4226_CR1","doi-asserted-by":"publisher","first-page":"4104","DOI":"10.1109\/TNNLS.2019.2952186","volume":"31","author":"X Li","year":"2020","unstructured":"Li X, Zhang W, Fang J A, et al. Event-triggered exponential synchronization for complex-valued memristive neural networks with time-varying delays. IEEE Trans Neural Netw Learn Syst, 2020, 31: 4104\u20134116","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"4226_CR2","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1109\/TCYB.2020.2983481","volume":"51","author":"S Wang","year":"2021","unstructured":"Wang S, Cao Y, Guo Z, et al. Periodic event-triggered synchronization of multiple memristive neural networks with switching topologies and parameter mismatch. IEEE Trans Cybern, 2021, 51: 427\u2013437","journal-title":"IEEE Trans Cybern"},{"key":"4226_CR3","doi-asserted-by":"publisher","first-page":"2746","DOI":"10.1109\/TNSE.2020.2985409","volume":"7","author":"S Wang","year":"2020","unstructured":"Wang S, Cao Y, Wen S, et al. Projective synchroniztion of neural networks via continuous\/periodic event-based sampling algorithms. IEEE Trans Netw Sci Eng, 2020, 7: 2746\u20132754","journal-title":"IEEE Trans Netw Sci Eng"},{"key":"4226_CR4","doi-asserted-by":"publisher","first-page":"3580","DOI":"10.1109\/TNSE.2022.3177718","volume":"9","author":"Z Xu","year":"2022","unstructured":"Xu Z, Tang R, Sun Y, et al. Secure synchronization of coupled systems via double event-triggering mechanisms with actuator fault. IEEE Trans Netw Sci Eng, 2022, 9: 3580\u20133589","journal-title":"IEEE Trans Netw Sci Eng"},{"key":"4226_CR5","doi-asserted-by":"publisher","first-page":"192202","DOI":"10.1007\/s11432-020-3144-6","volume":"64","author":"J P Yu","year":"2021","unstructured":"Yu J P, Shi P, Chen X K, et al. Finite-time command filtered adaptive control for nonlinear systems via immersion and invariance. Sci China Inf Sci, 2021, 64: 192202","journal-title":"Sci China Inf Sci"},{"key":"4226_CR6","doi-asserted-by":"publisher","first-page":"1942","DOI":"10.1002\/rnc.3991","volume":"28","author":"S Shi","year":"2018","unstructured":"Shi S, Xu S, Yu X, et al. Finite-time tracking control of uncertain nonholonomic systems by state and output feedback. Int J Robust Nonlinear, 2018, 28: 1942\u20131959","journal-title":"Int J Robust Nonlinear"},{"key":"4226_CR7","doi-asserted-by":"publisher","first-page":"192201","DOI":"10.1007\/s11432-018-2727-5","volume":"63","author":"X L Xiong","year":"2020","unstructured":"Xiong X L, Yang X S, Cao J D, et al. Finite-time control for a class of hybrid systems via quantized intermittent control. Sci China Inf Sci, 2020, 63: 192201","journal-title":"Sci China Inf Sci"},{"key":"4226_CR8","doi-asserted-by":"publisher","first-page":"212201","DOI":"10.1007\/s11432-018-9846-y","volume":"62","author":"H F Hong","year":"2019","unstructured":"Hong H F, Wang H, Wang Z L, et al. Finite-time and fixed-time consensus problems for second-order multi-agent systems with reduced state information. Sci China Inf Sci, 2019, 62: 212201","journal-title":"Sci China Inf Sci"},{"key":"4226_CR9","doi-asserted-by":"publisher","first-page":"2212","DOI":"10.1109\/TNSE.2023.3243610","volume":"10","author":"L H Zhao","year":"2023","unstructured":"Zhao L H, Wen S, Guo Z, et al. Finite-time nonchattering synchronization of coupled neural networks with multi-weights. IEEE Trans Netw Sci Eng, 2023, 10: 2212\u20132225","journal-title":"IEEE Trans Netw Sci Eng"},{"key":"4226_CR10","first-page":"4957","volume":"68","author":"L Wang","year":"2021","unstructured":"Wang L, Jiang S, Ge M F, et al. Finite-\/fixed-time synchronization of memristor chaotic systems and image encryption application. IEEE Trans Circ Syst I, 2021, 68: 4957\u20134969","journal-title":"IEEE Trans Circ Syst I"},{"key":"4226_CR11","first-page":"363","volume":"68","author":"X Song","year":"2021","unstructured":"Song X, Man J, Song S, et al. Finite\/fixed-time anti-synchronization of inconsistent Markovian quaternion-valued memristive neural networks with reaction-diffusion terms. IEEE Trans Circ Syst I, 2021, 68: 363\u2013375","journal-title":"IEEE Trans Circ Syst I"},{"key":"4226_CR12","first-page":"3609","volume":"10","author":"J Ping","year":"2023","unstructured":"Ping J, Zhu S, Shi M, et al. Event-triggered finite-time synchronization control for quaternion-valued memristive neural networks by a non-decomposition method. IEEE Trans Netw Sci Eng, 2023, 10: 3609\u20133619","journal-title":"IEEE Trans Netw Sci Eng"},{"key":"4226_CR13","doi-asserted-by":"publisher","first-page":"2944","DOI":"10.1109\/TCYB.2019.2953236","volume":"51","author":"S Gong","year":"2021","unstructured":"Gong S, Guo Z, Wen S, et al. Finite-time and fixed-time synchronization of coupled memristive neural networks with time delay. IEEE Trans Cybern, 2021, 51: 2944\u20132955","journal-title":"IEEE Trans Cybern"},{"key":"4226_CR14","doi-asserted-by":"publisher","first-page":"152202","DOI":"10.1007\/s11432-019-2897-9","volume":"64","author":"T Hou","year":"2021","unstructured":"Hou T, Liu Y Y, Deng F Q. Stability for discrete-time uncertain systems with infinite Markov jump and time-delay. Sci China Inf Sci, 2021, 64: 152202","journal-title":"Sci China Inf Sci"},{"key":"4226_CR15","doi-asserted-by":"publisher","first-page":"132202","DOI":"10.1007\/s11432-019-2678-2","volume":"63","author":"W B Xiao","year":"2020","unstructured":"Xiao W B, Cao L, Li H Y, et al. Observer-based adaptive consensus control for nonlinear multi-agent systems with time-delay. Sci China Inf Sci, 2020, 63: 132202","journal-title":"Sci China Inf Sci"},{"key":"4226_CR16","doi-asserted-by":"publisher","first-page":"1944","DOI":"10.1016\/j.automatica.2014.05.010","volume":"50","author":"D Efimov","year":"2014","unstructured":"Efimov D, Polyakov A, Fridman E, et al. Comments on finite-time stability of time-delay systems. Automatica, 2014, 50: 1944\u20131947","journal-title":"Automatica"},{"key":"4226_CR17","doi-asserted-by":"publisher","first-page":"3938","DOI":"10.1109\/TNNLS.2021.3054967","volume":"33","author":"T Yu","year":"2022","unstructured":"Yu T, Cao J, Rutkowski L, et al. Finite-time synchronization of complex-valued memristive-based neural networks via hybrid control. IEEE Trans Neural Netw Learn Syst, 2022, 33: 3938\u20133947","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"4226_CR18","doi-asserted-by":"publisher","first-page":"780","DOI":"10.1109\/TNSE.2021.3052255","volume":"8","author":"R Wei","year":"2021","unstructured":"Wei R, Cao J, Kurths J. Fixed-time output synchronization of coupled reaction-diffusion neural networks with delayed output couplings. IEEE Trans Netw Sci Eng, 2021, 8: 780\u2013789","journal-title":"IEEE Trans Netw Sci Eng"},{"key":"4226_CR19","doi-asserted-by":"publisher","first-page":"2358","DOI":"10.1109\/TCYB.2021.3117945","volume":"53","author":"F Kong","year":"2023","unstructured":"Kong F, Zhu Q, Huang T. New fixed-time stability criteria of time-varying delayed discontinuous systems and application to discontinuous neutral-type neural networks. IEEE Trans Cybern, 2023, 53: 2358\u20132367","journal-title":"IEEE Trans Cybern"},{"key":"4226_CR20","doi-asserted-by":"publisher","first-page":"8516","DOI":"10.1109\/TNNLS.2022.3151478","volume":"34","author":"L Cheng","year":"2023","unstructured":"Cheng L, Tang F, Shi X, et al. Finite-time and fixed-time synchronization of delayed memristive neural networks via adaptive aperiodically intermittent adjustment strategy. IEEE Trans Neural Netw Learn Syst, 2023, 34: 8516\u20138530","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"4226_CR21","doi-asserted-by":"publisher","first-page":"86","DOI":"10.1016\/j.neunet.2022.01.005","volume":"148","author":"C Long","year":"2022","unstructured":"Long C, Zhang G, Zeng Z, et al. Finite-time stabilization of complex-valued neural networks with proportional delays and inertial terms: a non-separation approach. Neural Netws, 2022, 148: 86\u201395","journal-title":"Neural Netws"},{"key":"4226_CR22","doi-asserted-by":"publisher","first-page":"2276","DOI":"10.1109\/TNNLS.2022.3189625","volume":"35","author":"Z Zhang","year":"2024","unstructured":"Zhang Z, Wei X, Wang S, et al. Fixed-time pinning common synchronization and adaptive synchronization for delayed quaternion-valued neural networks. IEEE Trans Neural Netw Learn Syst, 2024, 35: 2276\u20132289","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"4226_CR23","doi-asserted-by":"publisher","first-page":"192","DOI":"10.1016\/j.neunet.2022.06.002","volume":"153","author":"C Zheng","year":"2022","unstructured":"Zheng C, Hu C, Yu J, et al. Fixed-time synchronization of discontinuous competitive neural networks with time-varying delays. Neural Netws, 2022, 153: 192\u2013203","journal-title":"Neural Netws"},{"key":"4226_CR24","doi-asserted-by":"publisher","first-page":"4956","DOI":"10.1109\/TNNLS.2019.2962006","volume":"31","author":"P Liu","year":"2020","unstructured":"Liu P, Zeng Z, Wang J. Asymptotic and finite-time cluster synchronization of coupled fractional-order neural networks with time delay. IEEE Trans Neural Netw Learn Syst, 2020, 31: 4956\u20134967","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"4226_CR25","doi-asserted-by":"publisher","first-page":"5460","DOI":"10.1109\/TFUZZ.2022.3179130","volume":"30","author":"X Hu","year":"2022","unstructured":"Hu X, Wang L, Zeng Z, et al. Settling-time estimation for finite-time stabilization of fractional-order quaternion-valued fuzzy NNs. IEEE Trans Fuzzy Syst, 2022, 30: 5460\u20135472","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"4226_CR26","doi-asserted-by":"publisher","first-page":"7475","DOI":"10.1109\/TNNLS.2021.3085253","volume":"33","author":"T Peng","year":"2022","unstructured":"Peng T, Qiu J, Lu J, et al. Finite-time and fixed-time synchronization of quaternion-valued neural networks with\/without mixed delays: an improved one-norm method. IEEE Trans Neural Netw Learn Syst, 2022, 33: 7475\u20137487","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"4226_CR27","doi-asserted-by":"publisher","first-page":"1436","DOI":"10.1109\/TFUZZ.2021.3059953","volume":"30","author":"Z Zhang","year":"2022","unstructured":"Zhang Z, Cao J. Finite-time synchronization for fuzzy inertial neural networks by maximum value approach. IEEE Trans Fuzzy Syst, 2022, 30: 1436\u20131446","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"4226_CR28","doi-asserted-by":"publisher","first-page":"5268","DOI":"10.1109\/TNNLS.2021.3069926","volume":"33","author":"R Tang","year":"2022","unstructured":"Tang R, Su H, Zou Y, et al. Finite-time synchronization of Markovian coupled neural networks with delays via intermittent quantized control: linear programming approach. IEEE Trans Neural Netw Learn Syst, 2022, 33: 5268\u20135278","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"4226_CR29","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/j.neunet.2020.04.009","volume":"127","author":"L Hua","year":"2020","unstructured":"Hua L, Zhong S, Shi K, et al. Further results on finite-time synchronization of delayed inertial memristive neural networks via a novel analysis method. Neural Netws, 2020, 127: 47\u201357","journal-title":"Neural Netws"},{"key":"4226_CR30","first-page":"1599","volume":"68","author":"L Hua","year":"2021","unstructured":"Hua L, Zhu H, Shi K, et al. Novel finite-time reliable control design for memristor-based inertial neural networks with mixed time-varying delays. IEEE Trans Circ Syst I, 2021, 68: 1599\u20131609","journal-title":"IEEE Trans Circ Syst I"},{"key":"4226_CR31","doi-asserted-by":"publisher","first-page":"2398","DOI":"10.1080\/00207179.2021.1912396","volume":"95","author":"Q Wang","year":"2022","unstructured":"Wang Q, Duan L, Wei H, et al. Finite-time anti-synchronisation of delayed Hopfield neural networks with discontinuous activations. Int J Control, 2022, 95: 2398\u20132405","journal-title":"Int J Control"},{"key":"4226_CR32","volume-title":"Differential Equations","author":"A Halanay","year":"1996","unstructured":"Halanay A. Differential Equations. New York: Academic, 1996"},{"key":"4226_CR33","doi-asserted-by":"publisher","first-page":"1508","DOI":"10.1109\/TNN.2011.2160987","volume":"22","author":"B Liu","year":"2011","unstructured":"Liu B, Lu W L, Chen T P. Generalized Halanay inequalities and their applications to neural networks with unbounded time-varying delays. IEEE Trans Neural Netw, 2011, 22: 1508\u20131513","journal-title":"IEEE Trans Neural Netw"},{"key":"4226_CR34","doi-asserted-by":"publisher","first-page":"5993","DOI":"10.1109\/TCYB.2019.2960762","volume":"51","author":"J Chen","year":"2021","unstructured":"Chen J, Chen B, Zeng Z, et al. Event-based synchronization for multiple neural networks with time delay and switching disconnected topology. IEEE Trans Cybern, 2021, 51: 5993\u20136003","journal-title":"IEEE Trans Cybern"},{"key":"4226_CR35","doi-asserted-by":"publisher","first-page":"428","DOI":"10.1109\/TNNLS.2022.3175027","volume":"35","author":"Y Chen","year":"2024","unstructured":"Chen Y, Zhu S, Shen M, et al. Event-based output quantized synchronization control for multiple delayed neural networks. IEEE Trans Neural Netw Learn Syst, 2024, 35: 428\u2013438","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"4226_CR36","doi-asserted-by":"publisher","first-page":"1226","DOI":"10.1109\/TAC.2021.3061986","volume":"67","author":"X Zhao","year":"2022","unstructured":"Zhao X, Deng F. Time-varying Halanay inequalities with application to stability and control of delayed stochastic systems. IEEE Trans Automat Contr, 2022, 67: 1226\u20131240","journal-title":"IEEE Trans Automat Contr"},{"key":"4226_CR37","doi-asserted-by":"publisher","first-page":"105469","DOI":"10.1016\/j.sysconle.2023.105469","volume":"173","author":"D Ruan","year":"2023","unstructured":"Ruan D, Guo X, Shi Y. Generalized Halanay inequalities for stability and dissipativity of stochastic functional differential equations. Syst Control Lett, 2023, 173: 105469","journal-title":"Syst Control Lett"},{"key":"4226_CR38","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1016\/j.neunet.2021.12.012","volume":"148","author":"T Peng","year":"2022","unstructured":"Peng T, Zhong J, Tu Z, et al. Finite-time synchronization of quaternion-valued neural networks with delays: a switching control method without decomposition. Neural Netws, 2022, 148: 37\u201347","journal-title":"Neural Netws"},{"key":"4226_CR39","doi-asserted-by":"publisher","first-page":"3739","DOI":"10.1109\/TSMC.2019.2931046","volume":"51","author":"S Yang","year":"2021","unstructured":"Yang S, Yu J, Hu C, et al. Finite-time synchronization of memristive neural networks with fractional-order. IEEE Trans Syst Man Cybern Syst, 2021, 51: 3739\u20133750","journal-title":"IEEE Trans Syst Man Cybern Syst"},{"key":"4226_CR40","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1016\/j.jmaa.2008.05.007","volume":"347","author":"L Wen","year":"2008","unstructured":"Wen L, Yu Y, Wang W. Generalized Halanay inequalities for dissipativity of Volterra functional differential equations. J Math Anal Appl, 2008, 347: 169\u2013178","journal-title":"J Math Anal Appl"},{"key":"4226_CR41","doi-asserted-by":"publisher","first-page":"881","DOI":"10.1016\/j.automatica.2004.11.036","volume":"41","author":"X Huang","year":"2005","unstructured":"Huang X, Lin W, Yang B. Global finite-time stabilization of a class of uncertain nonlinear systems. Automatica, 2005, 41: 881\u2013888","journal-title":"Automatica"},{"key":"4226_CR42","doi-asserted-by":"publisher","first-page":"2621","DOI":"10.1109\/TAC.2009.2029298","volume":"54","author":"Y J Shen","year":"2009","unstructured":"Shen Y J, Huang Y H. Uniformly observable and globally Lipschitzian nonlinear systems admit global finite-time observers. IEEE Trans Automat Contr, 2009, 54: 2621\u20132625","journal-title":"IEEE Trans Automat Contr"},{"key":"4226_CR43","doi-asserted-by":"publisher","first-page":"1841","DOI":"10.1109\/TNN.2007.902958","volume":"18","author":"H G Zhang","year":"2007","unstructured":"Zhang H G, Xie Y H, Wang Z L, et al. Adaptive synchronization between two different chaotic neural networks with time delay. IEEE Trans Neural Netw, 2007, 18: 1841\u20131845","journal-title":"IEEE Trans Neural Netw"},{"key":"4226_CR44","doi-asserted-by":"publisher","first-page":"3775","DOI":"10.1109\/TII.2018.2808966","volume":"14","author":"B Hu","year":"2018","unstructured":"Hu B, Guan Z H, Xiong N, et al. Intelligent impulsive synchronization of nonlinear interconnected neural networks for image protection. IEEE Trans Ind Inf, 2018, 14: 3775\u20133787","journal-title":"IEEE Trans Ind Inf"},{"key":"4226_CR45","doi-asserted-by":"publisher","first-page":"3334","DOI":"10.1109\/TNNLS.2019.2943548","volume":"31","author":"W He","year":"2020","unstructured":"He W, Luo T, Tang Y, et al. Secure communication based on quantized synchronization of chaotic neural networks under an event-triggered strategy. IEEE Trans Neural Netw Learn Syst, 2020, 31: 3334\u20133345","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"4226_CR46","doi-asserted-by":"publisher","first-page":"3004","DOI":"10.1109\/TCYB.2019.2957398","volume":"51","author":"J Xiao","year":"2021","unstructured":"Xiao J, Zeng Z, Wen S, et al. A unified framework design for finite-time and fixed-time synchronization of discontinuous neural networks. IEEE Trans Cybern, 2021, 51: 3004\u20133016","journal-title":"IEEE Trans Cybern"}],"container-title":["Science China Information Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11432-024-4226-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11432-024-4226-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11432-024-4226-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,6]],"date-time":"2025-04-06T18:33:27Z","timestamp":1743964407000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11432-024-4226-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,2]]},"references-count":46,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2025,9]]}},"alternative-id":["4226"],"URL":"https:\/\/doi.org\/10.1007\/s11432-024-4226-x","relation":{},"ISSN":["1674-733X","1869-1919"],"issn-type":[{"value":"1674-733X","type":"print"},{"value":"1869-1919","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,2]]},"assertion":[{"value":"23 April 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 July 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 November 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 April 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"192203"}}