{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T18:39:05Z","timestamp":1769020745929,"version":"3.49.0"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2020,11,21]],"date-time":"2020-11-21T00:00:00Z","timestamp":1605916800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,11,21]],"date-time":"2020-11-21T00:00:00Z","timestamp":1605916800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2021,3]]},"DOI":"10.1007\/s00500-020-05415-4","type":"journal-article","created":{"date-parts":[[2020,11,21]],"date-time":"2020-11-21T10:03:42Z","timestamp":1605953022000},"page":"3903-3911","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A novel condition for fixed-time stability and its application in controller design for robust fixed-time chaos stabilization against H\u00f6lder continuous uncertainties"],"prefix":"10.1007","volume":"25","author":[{"given":"Alireza","family":"Khanzadeh","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9679-1067","authenticated-orcid":false,"given":"Mahdi","family":"Pourgholi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Elham","family":"Amini Boroujeni","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,11,21]]},"reference":[{"issue":"2","key":"5415_CR1","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1007\/s10483-012-1540-7","volume":"33","author":"MP Aghababa","year":"2012","unstructured":"Aghababa MP, Aghababa HP (2012a) Finite-time stabilization of uncertain non-autonomous chaotic gyroscopes with nonlinear inputs. Appl Math Mech -Engl 33(2):155\u2013164","journal-title":"Appl Math Mech -Engl"},{"issue":"9","key":"5415_CR2","doi-asserted-by":"publisher","first-page":"2875","DOI":"10.1016\/j.jfranklin.2012.08.004","volume":"349","author":"MP Aghababa","year":"2012","unstructured":"Aghababa MP, Aghababa HP (2012b) Finite-time stabilization of a non-autonomous chaotic rotating mechanical system. J Franklin Inst 349(9):2875\u20132888","journal-title":"J Franklin Inst"},{"issue":"3","key":"5415_CR3","doi-asserted-by":"publisher","first-page":"436","DOI":"10.1177\/1077546312463715","volume":"20","author":"MP Aghababa","year":"2012","unstructured":"Aghababa MP, Aghababa HP (2012c) Finite-time stabilization of non-autonomous uncertain chaotic centrifugal flywheel governor systems with input nonlinearities. J Vib Contr 20(3):436\u2013446","journal-title":"J Vib Contr"},{"issue":"4","key":"5415_CR4","doi-asserted-by":"publisher","first-page":"1814","DOI":"10.1137\/060675861","volume":"47","author":"V Andrieu","year":"2008","unstructured":"Andrieu V, Praly L, Astolfi A (2008) Homogeneous approximation, recursive observer design, and output feedback. SIAM J Contr Optim 47(4):1814\u20131850","journal-title":"SIAM J Contr Optim"},{"key":"5415_CR5","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1016\/j.neucom.2014.12.033","volume":"155","author":"M Cai","year":"2015","unstructured":"Cai M, Xiang Z (2015) Adaptive neural finite-time control for a class of switched nonlinear systems. Neurocomputing 155:177\u2013185","journal-title":"Neurocomputing"},{"key":"5415_CR6","doi-asserted-by":"publisher","first-page":"262","DOI":"10.1016\/j.isatra.2015.07.005","volume":"58","author":"Q Chen","year":"2015","unstructured":"Chen Q, Ren X, Na J (2015) Robust finite-time chaos synchronization of uncertain permanent magnet synchronous motors. ISA Trans 58:262\u2013269","journal-title":"ISA Trans"},{"key":"5415_CR7","unstructured":"Cruz-Zavala E, Moreno JA, Fridman L (2010) Uniform second-order observer for mechanical systems. In: 11th international workshop on variable structure systems, Mexico City, Mexico, IEEE, 2010, pp 14\u201319"},{"issue":"14","key":"5415_CR8","doi-asserted-by":"publisher","first-page":"2165","DOI":"10.1049\/iet-cta.2014.1301","volume":"9","author":"M Defoort","year":"2015","unstructured":"Defoort M, Polyakov A, Demesure G, Djemai M (2015) Leader-follower fixed-time consensus for multi-agent systems with unknown non-linear inherent dynamics. IET Control Theory Appl 9(14):2165\u20132170","journal-title":"IET Control Theory Appl"},{"issue":"11","key":"5415_CR9","doi-asserted-by":"publisher","first-page":"2711","DOI":"10.1109\/TAC.2011.2159419","volume":"56","author":"H Du","year":"2011","unstructured":"Du H, Li S, Qian C (2011) Finite-time attitude tracking control of spacecraft with application to attitude synchronization. IEEE Trans Autom Control 56(11):2711\u20132717","journal-title":"IEEE Trans Autom Control"},{"key":"5415_CR10","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.sysconle.2016.03.006","volume":"93","author":"J Fu","year":"2016","unstructured":"Fu J, Wang J (2016) Fixed-time coordinated tracking for second-order multi-agent systems with bounded input uncertainties. Syst Control Lett 93:1\u201312","journal-title":"Syst Control Lett"},{"key":"5415_CR11","volume-title":"Inequalities","author":"GH Hardy","year":"1952","unstructured":"Hardy GH, Littlewood JE, Polya G (1952) Inequalities. Cambridge University Press, Cambridge"},{"issue":"7","key":"5415_CR12","doi-asserted-by":"publisher","first-page":"1464","DOI":"10.1109\/TSMC.2016.2623634","volume":"47","author":"H Hong","year":"2017","unstructured":"Hong H, Yu W, Wen G, Yu X (2017) Distributed robust fixed-time consensus in multi-agent systems with nonlinear dynamics and uncertain disturbances. IEEE Trans Syst Man Cybern Syst 47(7):1464\u20131473","journal-title":"IEEE Trans Syst Man Cybern Syst"},{"key":"5415_CR13","doi-asserted-by":"publisher","first-page":"292","DOI":"10.1016\/j.automatica.2014.10.093","volume":"51","author":"J Huang","year":"2015","unstructured":"Huang J, Wen C, Wang W, Song YD (2015) Adaptive finite-time consensus control of a group of uncertain nonlinear mechanical systems. Automatica 51:292\u2013301","journal-title":"Automatica"},{"key":"5415_CR14","doi-asserted-by":"publisher","first-page":"2637","DOI":"10.1007\/s11071-017-3400-x","volume":"88","author":"A Kanzadeh","year":"2017","unstructured":"Kanzadeh A, Pourgholi M (2017) Fixed-time sliding mode controller design for synchronization of complex dynamical networks. Nonlinear Dyn 88:2637\u20132649","journal-title":"Nonlinear Dyn"},{"key":"5415_CR15","doi-asserted-by":"crossref","unstructured":"Lopez-Ramirez F, Polyakov A, Efimov D, Perruquetti W (2016) Finite-time and fixed-time observers design via implicit Lyapunov function. In: European control conference, Aalborg, Denmark, IEEE, 2016, pp 289\u2013294","DOI":"10.1109\/ECC.2016.7810300"},{"issue":"1","key":"5415_CR16","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1007\/s11071-016-2675-7","volume":"85","author":"D Meng","year":"2016","unstructured":"Meng D, Zuo Z (2016) Signed-average consensus for networks of agents: a nonlinear fixed-time convergence protocol. Nonlinear Dyn 85(1):155\u2013165","journal-title":"Nonlinear Dyn"},{"key":"5415_CR17","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1016\/j.automatica.2016.01.011","volume":"66","author":"AJ Munoz-Vazquez","year":"2016","unstructured":"Munoz-Vazquez AJ, Parra-Vega V, Sanchez-Orta A (2016) Uniformly continuous differintegral sliding mode control of nonlinear systems subject to Holder disturbances. Automatica 66:179\u2013184","journal-title":"Automatica"},{"issue":"1","key":"5415_CR18","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1007\/s11071-016-2897-8","volume":"86","author":"J Ni","year":"2016","unstructured":"Ni J, Liu L, Liu C, Hu X, Shen T (2016) Fixed-time dynamic surface high-order sliding mode control for chaotic oscillation in power system. Nonlinear Dyn 86(1):401\u2013420","journal-title":"Nonlinear Dyn"},{"issue":"8","key":"5415_CR19","doi-asserted-by":"publisher","first-page":"2106","DOI":"10.1109\/TAC.2011.2179869","volume":"57","author":"A Polyakov","year":"2012","unstructured":"Polyakov A (2012) Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans Autom Control 57(8):2106\u20132110","journal-title":"IEEE Trans Autom Control"},{"key":"5415_CR20","doi-asserted-by":"crossref","unstructured":"Polyakov A (2012) Fixed-time stabilization of linear systems via sliding mode control. In: 12th International workshop on variable structure systems, Mumbai, Maharashtra, IEEE, 2012, pp 1\u20136","DOI":"10.1109\/VSS.2012.6163469"},{"issue":"4","key":"5415_CR21","doi-asserted-by":"publisher","first-page":"1831","DOI":"10.1016\/j.jfranklin.2014.01.002","volume":"351","author":"A Polyakov","year":"2014","unstructured":"Polyakov A, Fridman L (2014) Stability notions and Lyapunov functions for sliding mode control systems. J Franklin Inst 351(4):1831\u20131865","journal-title":"J Franklin Inst"},{"key":"5415_CR22","doi-asserted-by":"publisher","first-page":"332","DOI":"10.1016\/j.automatica.2014.10.082","volume":"51","author":"A Polyakov","year":"2015","unstructured":"Polyakov A, Efimov D, Perruquetti W (2015) Finite-time and fixed-time stabilization: implicit Lyapunov function approach. Automatica 51:332\u2013340","journal-title":"Automatica"},{"issue":"1","key":"5415_CR23","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1002\/rnc.3297","volume":"26","author":"A Polyakov","year":"2016","unstructured":"Polyakov A, Efimov D, Perruquetti W (2016) Robust stabilization of MIMO systems in finite\/fixed time. Int J Robust Nonlinear Control 26(1):69\u201390","journal-title":"Int J Robust Nonlinear Control"},{"key":"5415_CR24","doi-asserted-by":"crossref","unstructured":"Sanchez-Torres JD, Loukianov A (2014) A fixed-time second order sliding mode observer for a class of nonlinear systems. In: 13th International workshop on variable structure systems, Nantes, France, IEEE, 2014, pp 1\u20134","DOI":"10.1109\/VSS.2014.6881137"},{"key":"5415_CR25","doi-asserted-by":"crossref","unstructured":"Sanchez-Torres JD, Sanchez EN, Loukianov AG (2015) Predefined-time stability of dynamical systems with sliding modes. In: American control conference, IEEE, Chicago, IL, USA, 2015, pp 5842\u20135846","DOI":"10.1109\/ACC.2015.7172255"},{"key":"5415_CR26","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1016\/j.chaos.2018.05.020","volume":"113","author":"M Shirkavand","year":"2018","unstructured":"Shirkavand M, Pourgholi M (2018) Robust fixed-time synchronization of fractional order chaotic using free chattering nonsingular adaptive fractional sliding mode controller design. Chaos Solitons Fractals 113:135\u2013147","journal-title":"Chaos Solitons Fractals"},{"issue":"1\u20132","key":"5415_CR27","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1007\/s11071-013-0780-4","volume":"73","author":"H Sun","year":"2013","unstructured":"Sun H, Li S, Sun C (2013) Finite time integral sliding mode control of hypersonic vehicles. Nonlinear Dyn 73(1\u20132):229\u2013244","journal-title":"Nonlinear Dyn"},{"issue":"7","key":"5415_CR28","doi-asserted-by":"publisher","first-page":"1420","DOI":"10.1080\/00207179.2016.1207101","volume":"90","author":"BL Tian","year":"2017","unstructured":"Tian BL, Zuo ZY, Wang H (2017) Leader-follower fixed-time consensus of multi-agent systems with high-order integrator dynamics. Int J Control 90(7):1420\u20131427","journal-title":"Int J Control"},{"issue":"5","key":"5415_CR29","doi-asserted-by":"publisher","first-page":"1315","DOI":"10.1016\/j.chaos.2006.07.052","volume":"36","author":"G Tigan","year":"2008","unstructured":"Tigan G, Opris D (2008) Analysis of a 3D chaotic system. Chaos Solitons Fract 36(5):1315\u20131319","journal-title":"Chaos Solitons Fract"},{"key":"5415_CR30","doi-asserted-by":"publisher","first-page":"86","DOI":"10.1016\/j.neunet.2015.10.009","volume":"73","author":"Y Wan","year":"2016","unstructured":"Wan Y, Cao J, Wen G, Yu W (2016) Robust fixed-time synchronization of delayed Cohen-Grossberg neural networks. Neural Net 73:86\u201394","journal-title":"Neural Net"},{"issue":"2","key":"5415_CR31","doi-asserted-by":"publisher","first-page":"1321","DOI":"10.1007\/s11071-014-1518-7","volume":"78","author":"J Wang","year":"2014","unstructured":"Wang J, Chen X, Fu J (2014) Adaptive finite-time control of chaos in permanent magnet synchronous motor with uncertain parameters. Nonlinear Dyn 78(2):1321\u20131328","journal-title":"Nonlinear Dyn"},{"key":"5415_CR32","doi-asserted-by":"crossref","unstructured":"Yan X, Zuo Z, Yin L, Wang A, Wang H (2015) Chattering-free sliding mode control for MIMO nonlinear manipulator systems based on adaptive neural networks. In: IEEE 54th annual conference on decision and control, IEEE, Osaka, Japan, 2015, pp 6300\u20136305","DOI":"10.1109\/CDC.2015.7403211"},{"key":"5415_CR33","doi-asserted-by":"crossref","unstructured":"Yun H, Zongyu Z, Zhiguang S (2015) Fixed-time terminal sliding mode trajectory tracking control of quadrotor helicopter. In: Proceedings of 2015 34th Chinese control conference, IEEE, Hangzhou, China, 2015, pp 4361\u20134366","DOI":"10.1109\/ChiCC.2015.7260315"},{"issue":"4","key":"5415_CR34","doi-asserted-by":"publisher","first-page":"1683","DOI":"10.1007\/s11071-015-2269-9","volume":"82","author":"B Zhang","year":"2015","unstructured":"Zhang B, Jia Y (2015) Fixed-time consensus protocols for multi-agent systems with linear and nonlinear state measurements. Nonlinear Dyn 82(4):1683\u20131690","journal-title":"Nonlinear Dyn"},{"issue":"9","key":"5415_CR35","doi-asserted-by":"publisher","first-page":"2540","DOI":"10.1016\/j.cnsns.2013.01.002","volume":"18","author":"S Zhankui","year":"2013","unstructured":"Zhankui S, Sun K (2013) Nonlinear and chaos control of a micro-electro-mechanical system by using second-order fast terminal sliding mode control. Commun Nonlinear Sci Numer Simulat 18(9):2540\u20132548","journal-title":"Commun Nonlinear Sci Numer Simulat"},{"key":"5415_CR36","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1016\/j.automatica.2015.01.021","volume":"54","author":"Z Zuo","year":"2015","unstructured":"Zuo Z (2015) Nonsingular fixed-time consensus tracking for second-order multi-agent systems. Automatica 54:305\u2013309","journal-title":"Automatica"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-020-05415-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00500-020-05415-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-020-05415-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,26]],"date-time":"2021-02-26T15:30:43Z","timestamp":1614353443000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00500-020-05415-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,21]]},"references-count":36,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2021,3]]}},"alternative-id":["5415"],"URL":"https:\/\/doi.org\/10.1007\/s00500-020-05415-4","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11,21]]},"assertion":[{"value":"21 November 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"The authors declare that they have no conflict of interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This article does not contain any studies with human participants or animals performed by any of the authors.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Human and animal rights"}},{"value":"Informed consent was obtained from all individual participants included in the study.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Informed consent"}}]}}