{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T11:57:16Z","timestamp":1774871836610,"version":"3.50.1"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2015,10,27]],"date-time":"2015-10-27T00:00:00Z","timestamp":1445904000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int. J. Mach. Learn. &amp; Cyber."],"published-print":{"date-parts":[[2016,8]]},"DOI":"10.1007\/s13042-015-0447-1","type":"journal-article","created":{"date-parts":[[2015,10,27]],"date-time":"2015-10-27T10:27:39Z","timestamp":1445941659000},"page":"641-652","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Exponential state estimation for Markovian jumping neural networks with mixed time-varying delays and discontinuous activation functions"],"prefix":"10.1007","volume":"7","author":[{"given":"Huaiqin","family":"Wu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Leifei","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peifeng","family":"Niu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bolin","family":"Fang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,10,27]]},"reference":[{"key":"447_CR1","doi-asserted-by":"crossref","DOI":"10.1002\/0471427950","volume-title":"Static and dynamic neural networks","author":"MM Gupta","year":"2003","unstructured":"Gupta MM, Jin L, Homma N (2003) Static and dynamic neural networks. Wiley-Interscience, New York"},{"key":"447_CR2","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1007\/s11071-010-9926-9","volume":"66","author":"H Wu","year":"2011","unstructured":"Wu H, Tao F, Qin L, Shi R, He L (2011) Robust exponential stability for interval neural networks with delays and non-Lipschitz activation functions. Nonlinear Dyn 66:479\u2013487","journal-title":"Nonlinear Dyn"},{"key":"447_CR3","doi-asserted-by":"crossref","first-page":"751","DOI":"10.1007\/s00521-014-1545-9","volume":"25","author":"R Raja","year":"2014","unstructured":"Raja R, Karthik Raja U, Samidurai R, Leelamani A (2014) Passivity analysis for uncertain discrete-time stochastic BAM neural networks with multiple time varying delays. Neural Comput Appl 25:751\u2013766","journal-title":"Neural Comput Appl"},{"key":"447_CR4","doi-asserted-by":"crossref","first-page":"2564","DOI":"10.1016\/j.apm.2008.07.022","volume":"33","author":"H Wu","year":"2009","unstructured":"Wu H, Shan C (2009) Stability analysis for periodic solution of BAM neural networks with discontinuous neuron activations and impulses. Appl Math Model 33:2564\u20132574","journal-title":"Appl Math Model"},{"key":"447_CR5","doi-asserted-by":"crossref","unstructured":"Karthik Raja U, Raja R, Samidurai R, Leelamani A (2013) Exponential stability for stochastic delayed recurrent neural networks with mixed time-varying delays and impulses: the continuous-time case. Phys Scr 87:1\u201311","DOI":"10.1088\/0031-8949\/87\/05\/055802"},{"key":"447_CR6","first-page":"1156","volume":"78","author":"R Raja","year":"2012","unstructured":"Raja R, Sakthivel R, Marshal Anthoni S (2012) Linear matrix inequality approach to stochastic stability of uncertain delayed BAM neural networks. IMA J Appl Math 78:1156\u20131178","journal-title":"IMA J Appl Math"},{"key":"447_CR7","doi-asserted-by":"crossref","first-page":"1421","DOI":"10.1109\/TCSI.2003.818614","volume":"50","author":"M Forti","year":"2003","unstructured":"Forti M, Nistri P (2003) Global convergence of neural networks with discontinuous neuron activations. IEEE Trans Circuits Syst 50:1421\u20131435","journal-title":"IEEE Trans Circuits Syst"},{"key":"447_CR8","doi-asserted-by":"crossref","first-page":"1717","DOI":"10.1016\/j.nonrwa.2008.02.024","volume":"10","author":"H Wu","year":"2009","unstructured":"Wu H (2009) Stability analysis for periodic solution of neural networks with discountiunous neuron activations. Nonlinear Anal: Real World Appl 10:1717\u20131729","journal-title":"Nonlinear Anal: Real World Appl"},{"key":"447_CR9","doi-asserted-by":"crossref","first-page":"3432","DOI":"10.1016\/j.ins.2009.06.006","volume":"179","author":"H Wu","year":"2009","unstructured":"Wu H (2009) Global stability analysis of a general class of discontinuous neural networks with linear growth activation functions. Inf Sci 179:3432\u20133441","journal-title":"Inf Sci"},{"key":"447_CR10","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.neunet.2012.04.009","volume":"33","author":"Z Cai","year":"2012","unstructured":"Cai Z, Huang L, Guo Z, Chen X (2012) On the periodic dynamics of a class of time-varying delayed neural networks via differential inclusions. Neural Netw 33:97\u2013113","journal-title":"Neural Netw"},{"key":"447_CR11","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1016\/j.ins.2012.07.040","volume":"220","author":"S Qin","year":"2013","unstructured":"Qin S, Xue X, Wang P (2013) Global exponential stability of almost periodic solution of delayed neural networks with discontinuous activations. Inf Sci 220:367\u2013378","journal-title":"Inf Sci"},{"key":"447_CR12","doi-asserted-by":"crossref","first-page":"1157","DOI":"10.1016\/j.chaos.2012.05.009","volume":"45","author":"J Wang","year":"2012","unstructured":"Wang J, Huang L (2012) Almost periodicity for a class of delayed Cohen\u2013Grossberg neural networks with discontinuous activations. Chaos Solitons Fractals 45:1157\u20131170","journal-title":"Chaos Solitons Fractals"},{"key":"447_CR13","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/j.ins.2011.08.021","volume":"183","author":"J Liu","year":"2012","unstructured":"Liu J, Liu X, Xie W (2012) Global convergence of neural networks with mixed time-varying delays and discontinuous neuron activations. Inf Sci 183:92\u2013105","journal-title":"Inf Sci"},{"key":"447_CR14","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1016\/j.physd.2005.12.006","volume":"214","author":"M Forti","year":"2006","unstructured":"Forti M, Grazzini M, Nistri P (2006) Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipschitz activations. Physica D 214:88\u201389","journal-title":"Physica D"},{"key":"447_CR15","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1002\/cta.381","volume":"35","author":"M Forti","year":"2007","unstructured":"Forti M (2007) M-matrices and global convergence of discontinuous neural networks. Int J Circuit Theory Appl 35:105\u2013130","journal-title":"Int J Circuit Theory Appl"},{"key":"447_CR16","doi-asserted-by":"crossref","first-page":"1110","DOI":"10.1109\/TNN.2010.2048759","volume":"21","author":"W Allegretto","year":"2010","unstructured":"Allegretto W, Papini D, Forti M (2010) Common asymptotic behavior of solutions and almost periodicity for discontinuous, delayed, and impulsive neural networks. IEEE Trans Neural Netw 21:1110\u20131125","journal-title":"IEEE Trans Neural Netw"},{"key":"447_CR17","doi-asserted-by":"crossref","first-page":"6174","DOI":"10.1016\/j.eswa.2011.11.111","volume":"39","author":"Z Wu","year":"2012","unstructured":"Wu Z, Shi P, Su H, Chu J (2012) Stability analysis for discrete-time Markovian jump neural networks with mixed time-delays. Expert Syst Appl 39:6174\u20136181","journal-title":"Expert Syst Appl"},{"key":"447_CR18","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.neucom.2012.04.003","volume":"94","author":"Y Liu","year":"2012","unstructured":"Liu Y, Wang Z, Liu X (2012) Stability analysis for a class of neutral-type neural networks with Markovian jumping parameters and mode-dependent mixed delays. Neurocomputing 94:46\u201353","journal-title":"Neurocomputing"},{"key":"447_CR19","doi-asserted-by":"crossref","first-page":"1314","DOI":"10.1109\/TNN.2010.2054108","volume":"21","author":"Q Zhu","year":"2010","unstructured":"Zhu Q, Cao J (2010) Robust exponential stability of Markovian jump impulsive stochastic Cohen\u2013Grossberg neural networks with mixed time delays. IEEE Trans Neural Netw 21:1314\u20131325","journal-title":"IEEE Trans Neural Netw"},{"key":"447_CR20","doi-asserted-by":"crossref","first-page":"1566","DOI":"10.1109\/TNN.2011.2163203","volume":"22","author":"Z Wu","year":"2011","unstructured":"Wu Z, Shi P, Su H, Chu J (2011) Passivity analysis for discrete-time stochastic Markovian jump neural networks with mixed time delays. IEEE Trans Neural Netw 22:1566\u20131575","journal-title":"IEEE Trans Neural Netw"},{"key":"447_CR21","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1109\/TNNLS.2011.2177671","volume":"23","author":"X Yang","year":"2012","unstructured":"Yang X, Cao J, Lu J (2012) Synchronization of Markovian coupled neural networks with nonidentical node-delays and random coupling strengths. IEEE Trans Neural Netw Learn Syst 23:60\u201371","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"447_CR22","doi-asserted-by":"crossref","first-page":"1273","DOI":"10.1016\/j.cnsns.2011.07.024","volume":"17","author":"C Zheng","year":"2012","unstructured":"Zheng C, Zhou F, Wang Z (2012) Stochastic exponential synchronization of jumping chaotic neural networks with mixed delays. Commun Nonlinear Sci Numer Simul 17:1273\u20131291","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"447_CR23","first-page":"169","volume":"141","author":"L Jin","year":"1994","unstructured":"Jin L, Nikiforuk PN, Gupta MM (1994) Adaptive control of discrete-time nonlinear systems using recurrent neural networks. IEE Proc: Control Theory Appl 141:169\u2013176","journal-title":"IEE Proc: Control Theory Appl"},{"key":"447_CR24","doi-asserted-by":"crossref","first-page":"1421","DOI":"10.1007\/s11071-012-0544-6","volume":"70","author":"S Lakshmanan","year":"2012","unstructured":"Lakshmanan S, Park J, Ji D, Jung H, Nagamani G (2012) State estimation of neural networks with time-varying delays and Markovian jumping parameter based on passivity theory. Nonlinear Dyn 70:1421\u20131434","journal-title":"Nonlinear Dyn"},{"key":"447_CR25","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.neunet.2008.09.015","volume":"22","author":"Z Wang","year":"2009","unstructured":"Wang Z, Liu Y, Liu X (2009) State estimation for jumping recurrent neural networks with discrete and distributed delays. Neural Netw 22:41\u201348","journal-title":"Neural Netw"},{"key":"447_CR26","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.neunet.2012.08.005","volume":"35","author":"D Zhang","year":"2012","unstructured":"Zhang D, Yu L (2012) Exponential state estimation for Markovian jumping neural networks with time-varying discrete and distributed delays. Neural Netw 35:103\u2013111","journal-title":"Neural Netw"},{"key":"447_CR27","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1007\/s11071-009-9623-8","volume":"60","author":"P Balasubramaniam","year":"2010","unstructured":"Balasubramaniam P, Lakshmanan S, Jeeva Sathya Theesar S (2010) State estimation for Markovian jumping recurrent neural networks with interval time-varying delays. Nonlinear Dyn 60:661\u2013675","journal-title":"Nonlinear Dyn"},{"key":"447_CR28","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1016\/j.neunet.2012.10.002","volume":"36","author":"H Huang","year":"2012","unstructured":"Huang H, Huang T, Chen X (2012) Global exponential estimates of delayed stochastic neural networks with Markovian switching. Neural Netw 36:136\u2013145","journal-title":"Neural Netw"},{"key":"447_CR29","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.neunet.2011.08.002","volume":"25","author":"Y Chen","year":"2012","unstructured":"Chen Y, Zheng W (2012) Stochastic state estimation for neural networks with distributed delays and Markovian jump. Neural Netw 25:14\u201320","journal-title":"Neural Netw"},{"key":"447_CR30","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1007\/s11071-013-0783-1","volume":"73","author":"J Hu","year":"2013","unstructured":"Hu J, Li N, Liu X, Zhang G (2013) Sampled-data state estimation for delayed neural networks with Markovian jumping parameters. Nonlinear Dyn 73:275\u2013284","journal-title":"Nonlinear Dyn"},{"key":"447_CR31","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.neunet.2013.05.001","volume":"46","author":"TH Lee","year":"2013","unstructured":"Lee TH, Park JH, Kwon OM (2013) Stochastic sampled-data control for state estimation of time-varying delayed neural networks. Neural Netw 46:99\u2013108","journal-title":"Neural Netw"},{"key":"447_CR32","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1007\/s11071-011-0286-x","volume":"69","author":"N Li","year":"2012","unstructured":"Li N, Hu J, Hu J, Li L (2012) Exponential state estimation for delayed recurrent neural nebtworks with sampled-data. Nonlinear Dyn 69:555\u2013564","journal-title":"Nonlinear Dyn"},{"key":"447_CR33","doi-asserted-by":"crossref","first-page":"1425","DOI":"10.1109\/TSMCB.2009.2039478","volume":"40","author":"X Liu","year":"2010","unstructured":"Liu X, Cao J (2010) Robust state estimations for neural networks with discontinuous activations. IEEE Trans Syst Man Cybern Part B 40:1425\u20131437","journal-title":"IEEE Trans Syst Man Cybern Part B"},{"key":"447_CR34","volume-title":"Differential equations with discontinuous right-hand side, mathematics and its applications (Soviet Series)","author":"AF Filippov","year":"1984","unstructured":"Filippov AF (1984) Differential equations with discontinuous right-hand side, mathematics and its applications (Soviet Series). Kluwer Academic, Boston"},{"key":"447_CR35","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-02431-3","volume-title":"Variational analysis","author":"RT Rockafellar","year":"1998","unstructured":"Rockafellar RT, Wets RJB (1998) Variational analysis. Springer, Berlin"},{"key":"447_CR36","volume-title":"Oprimization and non-smooth analysis","author":"FH Clarke","year":"1983","unstructured":"Clarke FH (1983) Oprimization and non-smooth analysis. Wiley, New York"},{"key":"447_CR37","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-69512-4","volume-title":"Differential inclusions","author":"JP Aubin","year":"1984","unstructured":"Aubin JP, Cellina A (1984) Differential inclusions. Springer, Berlin"},{"key":"447_CR38","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970777","volume-title":"Linear matrix inequalities in system and control theory","author":"S Boyd","year":"1994","unstructured":"Boyd S, Ghaoui LF, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM, Philadelphia"},{"key":"447_CR39","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.neunet.2013.04.014","volume":"46","author":"H Huang","year":"2013","unstructured":"Huang H, Huang T, Chen X (2013) A mode-dependent approach to state estimation of recurrent neural networks with Markovian jumping parameters and mixed delays. Neural Netw 46:50\u201361","journal-title":"Neural Netw"}],"container-title":["International Journal of Machine Learning and Cybernetics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-015-0447-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s13042-015-0447-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-015-0447-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T14:31:21Z","timestamp":1559485881000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s13042-015-0447-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,10,27]]},"references-count":39,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2016,8]]}},"alternative-id":["447"],"URL":"https:\/\/doi.org\/10.1007\/s13042-015-0447-1","relation":{},"ISSN":["1868-8071","1868-808X"],"issn-type":[{"value":"1868-8071","type":"print"},{"value":"1868-808X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,10,27]]}}}