{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T08:06:37Z","timestamp":1780473997935,"version":"3.54.1"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2025,11,27]],"date-time":"2025-11-27T00:00:00Z","timestamp":1764201600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,11,27]],"date-time":"2025-11-27T00:00:00Z","timestamp":1764201600000},"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":["62173165"],"award-info":[{"award-number":["62173165"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62303342"],"award-info":[{"award-number":["62303342"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Circuits Syst Signal Process"],"published-print":{"date-parts":[[2026,6]]},"DOI":"10.1007\/s00034-025-03426-w","type":"journal-article","created":{"date-parts":[[2025,11,27]],"date-time":"2025-11-27T05:09:50Z","timestamp":1764220190000},"page":"4411-4432","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Event-Triggered Consensus Control of Two-Layer Networks with Switching Topologies: An Observer-Based Approach"],"prefix":"10.1007","volume":"45","author":[{"given":"Xiaoqian","family":"Wang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0228-6167","authenticated-orcid":false,"given":"Jun","family":"Chen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qi","family":"Chang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,11,27]]},"reference":[{"key":"3426_CR1","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1146\/annurev-conmatphys-031218-013259","volume":"10","author":"A Aleta","year":"2019","unstructured":"A. Aleta, Y. Moreno, Multilayer networks in a nutshell. Annu. Rev. Condensed Matter Phys. 10, 45\u201362 (2019)","journal-title":"Annu. Rev. Condensed Matter Phys."},{"key":"3426_CR2","volume-title":"Nonnegative Matrices in the Mathematical Sciences","author":"A Berman","year":"1979","unstructured":"A. Berman, R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences (Academic, New York, 1979)"},{"issue":"4","key":"3426_CR3","doi-asserted-by":"publisher","first-page":"1184","DOI":"10.1109\/59.898088","volume":"15","author":"M Ceraolo","year":"2020","unstructured":"M. Ceraolo, New dynamical models of lead-acid batteries. IEEE Trans. Power Syst. 15(4), 1184\u20131190 (2020)","journal-title":"IEEE Trans. Power Syst."},{"issue":"1","key":"3426_CR4","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1080\/00207179608921833","volume":"63","author":"J Chen","year":"1996","unstructured":"J. Chen, R. Patton, H.Y. Zhang, Design of unknown input observers and robust fault detection filters. Int. J. Control 63(1), 85\u2013105 (1996)","journal-title":"Int. J. Control"},{"key":"3426_CR5","doi-asserted-by":"publisher","first-page":"675","DOI":"10.1109\/TNNLS.2019.2909350","volume":"31","author":"J Chen","year":"2020","unstructured":"J. Chen, X.M. Zhang, J.H. Park, Improved stability criteria for delayed neural networks using a quadratic function negative-definiteness approach. IEEE Trans. Neur. Net. Lear. 31, 675\u2013684 (2020)","journal-title":"IEEE Trans. Neur. Net. Lear."},{"issue":"3","key":"3426_CR6","doi-asserted-by":"publisher","first-page":"606","DOI":"10.1109\/9.280770","volume":"39","author":"M Darouach","year":"1994","unstructured":"M. Darouach, M. Zasadzinski, S. Xu, Full-order observers for linear systems with unknown inputs. IEEE Trans. Autom. Control 39(3), 606\u2013609 (1994)","journal-title":"IEEE Trans. Autom. Control"},{"key":"3426_CR7","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1016\/j.neucom.2019.01.113","volume":"416","author":"T Dong","year":"2020","unstructured":"T. Dong, Y. Gong, Leader-following secure consensus for second-order multi-agent systems with nonlinear dynamics and eventtriggered control strategy under DoS attack. Neurocomputing 416, 95\u2013102 (2020)","journal-title":"Neurocomputing"},{"issue":"2","key":"3426_CR8","doi-asserted-by":"publisher","first-page":"671","DOI":"10.1016\/j.automatica.2012.11.010","volume":"49","author":"Y Fan","year":"2013","unstructured":"Y. Fan, G. Feng, Y. Wang, C. Song, Distributed event-triggered control of multi-agent systems with combinational measurements. Automatica 49(2), 671\u2013675 (2013)","journal-title":"Automatica"},{"issue":"3","key":"3426_CR9","doi-asserted-by":"publisher","first-page":"741","DOI":"10.1109\/TCST.2019.2892032","volume":"28","author":"Z Feng","year":"2020","unstructured":"Z. Feng, G. Hu, Secure cooperative event-triggered control of linear multiagent systems under DoS attacks. IEEE Trans. Control Syst. Technol. 28(3), 741\u2013752 (2020)","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"3426_CR10","doi-asserted-by":"publisher","first-page":"7576","DOI":"10.1007\/s00034-024-02771-6","volume":"43","author":"YH Ju","year":"2024","unstructured":"Y.H. Ju, F.W. Meng, Y.G. Sun, Practical exponential stability of positive switched linear system and its application in practical consensus of multi-agent system. Circ. Syst. Signal Pr. 43, 7576\u20137591 (2024)","journal-title":"Circ. Syst. Signal Pr."},{"issue":"1","key":"3426_CR11","first-page":"213","volume":"57","author":"Z Li","year":"2010","unstructured":"Z. Li, Z. Duan, G. Chen, L. Huang, Consensus of multiagent systems and synchronization of complex networks: a unified viewpoint. IEEE Trans. Circuits Syst. I: Reg. Papers 57(1), 213\u2013224 (2010)","journal-title":"IEEE Trans. Circuits Syst. I: Reg. Papers"},{"key":"3426_CR12","doi-asserted-by":"publisher","first-page":"862","DOI":"10.1007\/s00034-024-02883-z","volume":"44","author":"LW Li","year":"2025","unstructured":"L.W. Li, Y.F. Lu, F.X. Wang, X.G. Liu, Mittag-leffler stability and synchronization of multi-delayed fractional neural networks via Halanay inequality. Circ. Syst. Signal Pr. 44, 862\u2013887 (2025)","journal-title":"Circ. Syst. Signal Pr."},{"issue":"3","key":"3426_CR13","doi-asserted-by":"publisher","first-page":"1124","DOI":"10.1109\/TNET.2019.2911272","volume":"27","author":"Z Li","year":"2019","unstructured":"Z. Li, H. Wan, Z. Pang, Q. Chen, M. Gu, An enhanced reconfiguration for deterministic transmission in time-triggered networks. IEEE\/ACM Trans. Netw. 27(3), 1124\u20131137 (2019)","journal-title":"IEEE\/ACM Trans. Netw."},{"key":"3426_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0017-8","volume-title":"Switching in Systems and Control","author":"D Liberzon","year":"2003","unstructured":"D. Liberzon, Switching in Systems and Control (Springer, Boston, 2003)"},{"issue":"3","key":"3426_CR15","first-page":"1087","volume":"32","author":"SY Mao","year":"2024","unstructured":"S.Y. Mao, X.S. Yang, M.L. Wang, W.X. Zheng, Secure stabilization of switched T-S fuzzy systems with mixed delay via mode-dependent event-triggered control. IEEE Trans. Syst. Man. Cybern. Syst. 32(3), 1087\u20131097 (2024)","journal-title":"IEEE Trans. Syst. Man. Cybern. Syst."},{"issue":"1","key":"3426_CR16","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1109\/JPROC.2006.887293","volume":"95","author":"RS Olfati","year":"2007","unstructured":"R.S. Olfati, J.A. Fa, R.M. Murray, Consensus and cooperation in networked multi-agent systems. Proc. IEEE 95(1), 215\u2013233 (2007)","journal-title":"Proc. IEEE"},{"issue":"9","key":"3426_CR17","doi-asserted-by":"publisher","first-page":"1520","DOI":"10.1109\/TAC.2004.834113","volume":"49","author":"RS Olfati","year":"2004","unstructured":"R.S. Olfati, R.M. Murray, Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control 49(9), 1520\u20131533 (2004)","journal-title":"IEEE Trans. Autom. Control"},{"key":"3426_CR18","first-page":"1282","volume":"21","author":"JF Padgett","year":"1994","unstructured":"J.F. Padgett, Marriage and elite structure in renaissance Florence. Soc. Sci. History Associat. 21, 1282\u20131500 (1994)","journal-title":"Soc. Sci. History Associat."},{"key":"3426_CR19","volume-title":"Recent Advances in Control Problems of Dynamical Systems and Networks","author":"JH Park","year":"2020","unstructured":"J.H. Park, Recent Advances in Control Problems of Dynamical Systems and Networks (Springer-Nature, Cham, Switzerland, 2020)"},{"issue":"7","key":"3426_CR20","doi-asserted-by":"publisher","first-page":"4545","DOI":"10.1109\/TCYB.2022.3208156","volume":"53","author":"QH Qi","year":"2023","unstructured":"Q.H. Qi, X.S. Yang, X.L. Xu, M.J. Zhang, T.W. Huang, Novel LKF method on H-infinity synchronization of switched time-delay systems. IEEE Trans. Cybernetics 53(7), 4545\u20134554 (2023)","journal-title":"IEEE Trans. Cybernetics"},{"key":"3426_CR21","doi-asserted-by":"publisher","first-page":"655","DOI":"10.1109\/TAC.2005.846556","volume":"50","author":"W Ren","year":"2005","unstructured":"W. Ren, R.W. Beard, Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Trans. Autom. Control 50, 655\u2013661 (2005)","journal-title":"IEEE Trans. Autom. Control"},{"key":"3426_CR22","doi-asserted-by":"crossref","unstructured":"W. Ren, Y.C. Cao, Distributed coordination of multi-agent networks: emergent problems, models, and issues. Springer Science and Business Media (2011)","DOI":"10.1007\/978-0-85729-169-1"},{"key":"3426_CR23","doi-asserted-by":"publisher","first-page":"168","DOI":"10.1016\/j.neucom.2021.03.009","volume":"450","author":"J Ren","year":"2021","unstructured":"J. Ren, Q. Song, Y. Gao, M. Zhao, G. Lu, Leader-following consensus of delayed neural networks under multi-layer signed graphs. Neurocomputing 450, 168\u2013182 (2021)","journal-title":"Neurocomputing"},{"issue":"5","key":"3426_CR24","doi-asserted-by":"publisher","first-page":"2911","DOI":"10.1109\/TSMC.2021.3055398","volume":"52","author":"LN Rong","year":"2022","unstructured":"L.N. Rong, X. Liu, G.P. Jiang, S.Y. Xu, Event-driven multiagent consensus disturbance rejection with input uncertainties via adaptive protocols. IEEE Trans. Syst. Man. Cybern. Syst. 52(5), 2911\u20132919 (2022)","journal-title":"IEEE Trans. Syst. Man. Cybern. Syst."},{"issue":"3","key":"3426_CR25","doi-asserted-by":"publisher","first-page":"2250047","DOI":"10.1142\/S0218348X22500475","volume":"30","author":"XQ Wang","year":"2022","unstructured":"X.Q. Wang, L. Wang, Consensus analysis in hierarchical networked systems. Fractals 30(3), 2250047 (2022)","journal-title":"Fractals"},{"issue":"1","key":"3426_CR26","doi-asserted-by":"publisher","first-page":"630","DOI":"10.1109\/TCYB.2020.2981518","volume":"53","author":"PJ Wang","year":"2022","unstructured":"P.J. Wang, G.H. Wen, T. Huang, W.W. Yu, Y. Ren, Observer-based consensus protocol for directed switching networks with a leader of nonzero inputs. IEEE Trans. Cybernetics 53(1), 630\u2013640 (2022)","journal-title":"IEEE Trans. Cybernetics"},{"issue":"3","key":"3426_CR27","first-page":"1141","volume":"66","author":"PJ Wang","year":"2019","unstructured":"P.J. Wang, G.H. Wen, X.H. Yu, W.W. Yu, T. Huang, Synchronization of multi-layer networks: from node-to-node synchronization to complete synchronization. IEEE Trans. Circuits Syst. I: Reg. Papers 66(3), 1141\u20131152 (2019)","journal-title":"IEEE Trans. Circuits Syst. I: Reg. Papers"},{"issue":"1","key":"3426_CR28","doi-asserted-by":"publisher","first-page":"254","DOI":"10.1109\/TCNS.2019.2903005","volume":"7","author":"PJ Wang","year":"2020","unstructured":"P.J. Wang, G.H. Wen, X. Yu, W.W. Yu, Y. Lv, Consensus disturbance rejection for linear multiagent systems with directed switching communication topologies. IEEE T. Control Netw. 7(1), 254\u2013265 (2020)","journal-title":"IEEE T. Control Netw."},{"issue":"5","key":"3426_CR29","doi-asserted-by":"publisher","first-page":"1886","DOI":"10.1002\/rnc.3990","volume":"28","author":"PJ Wang","year":"2018","unstructured":"P.J. Wang, W.W. Yu, X. Yu, Robust node-to-node consensus of linear multiagent systems with directed switching topologies subject to uncertain pinning communications. Int. J. Robust Nonlin. Control 28(5), 1886\u20131900 (2018)","journal-title":"Int. J. Robust Nonlin. Control"},{"issue":"2","key":"3426_CR30","doi-asserted-by":"publisher","first-page":"657","DOI":"10.1109\/TFUZZ.2024.3488015","volume":"33","author":"W Wu","year":"2025","unstructured":"W. Wu, S. Tong, Adaptive fuzzy distributed optimal FTC for nonlinear multiagent systems based multiplayer differential game. IEEE Trans. Fuzzy Syst. 33(2), 657\u2013668 (2025)","journal-title":"IEEE Trans. Fuzzy Syst."},{"issue":"10","key":"3426_CR31","doi-asserted-by":"publisher","first-page":"4201","DOI":"10.1109\/TFUZZ.2022.3145808","volume":"30","author":"XS Yang","year":"2022","unstructured":"X.S. Yang, G.Y. Feng, C.T. He, J.D. Cao, Event-triggered dynamic output quantization control of switched T-S fuzzy systems with unstable modes. IEEE Trans. Fuzzt. Syst. 30(10), 4201\u20134210 (2022)","journal-title":"IEEE Trans. Fuzzt. Syst."},{"issue":"9","key":"3426_CR32","first-page":"3759","volume":"70","author":"XS Yang","year":"2023","unstructured":"X.S. Yang, Q.H. Qi, P. Shi, Z.R. Xiang, L.B. Qing, Non-weighted L2-gain analysis for synchronization of switched nonlinear time-delay systems with random injection attacks. IEEE Trans. Circuits Syst. I: Reg. Papers 70(9), 3759\u20133769 (2023)","journal-title":"IEEE Trans. Circuits Syst. I: Reg. Papers"},{"key":"3426_CR33","doi-asserted-by":"publisher","first-page":"3500","DOI":"10.1007\/s00034-024-02646-w","volume":"43","author":"JS Yu","year":"2024","unstructured":"J.S. Yu, Z.J. Ma, K.Z. Li, M.Y. Chang, Event-triggered control of lag consensus for leader-following multi-agent systems with nonlinear dynamics. Circ. Syst. Signal Pr. 43, 3500\u20133515 (2024)","journal-title":"Circ. Syst. Signal Pr."},{"issue":"5","key":"3426_CR34","doi-asserted-by":"publisher","first-page":"2459","DOI":"10.1002\/asjc.2359","volume":"23","author":"YW Zhang","year":"2021","unstructured":"Y.W. Zhang, Piece-wise control of constant electromagnetic moments for spacecraft self- and soft-docking exploiting dynamics conservation. Asian J. Control 23(5), 2459\u20132473 (2021)","journal-title":"Asian J. Control"},{"issue":"9","key":"3426_CR35","doi-asserted-by":"publisher","first-page":"4885","DOI":"10.1109\/TIE.2013.2290757","volume":"61","author":"H Zhang","year":"2014","unstructured":"H. Zhang, G. Feng, H. Yan, Q. Chen, Observer-based output feedback event-triggered control for consensus of multi-Agent systems. IEEE T. Ind. Electron. 61(9), 4885\u20134894 (2014)","journal-title":"IEEE T. Ind. Electron."},{"key":"3426_CR36","doi-asserted-by":"publisher","first-page":"107124","DOI":"10.1016\/j.cnsns.2023.107124","volume":"119","author":"C Zhang","year":"2023","unstructured":"C. Zhang, C. Zhang, X.F. Zhang, F. Wang, Y. Liang, Dynamic event-triggered control for intra\/inter-layer synchronization in multi-layer networks. Commun. Nonlinear Sci. Numer. Simul. 119, 107124 (2023)","journal-title":"Commun. Nonlinear Sci. Numer. Simul."}],"container-title":["Circuits, Systems, and Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-025-03426-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00034-025-03426-w","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-025-03426-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T07:42:33Z","timestamp":1780472553000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00034-025-03426-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,27]]},"references-count":36,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2026,6]]}},"alternative-id":["3426"],"URL":"https:\/\/doi.org\/10.1007\/s00034-025-03426-w","relation":{},"ISSN":["0278-081X","1531-5878"],"issn-type":[{"value":"0278-081X","type":"print"},{"value":"1531-5878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,27]]},"assertion":[{"value":"11 March 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 November 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 November 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 November 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 have no Conflict of interest to declare.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}