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The proposed finite-time and fixed-time consensus algorithms guarantee that the MAS attains the NTSM surface in finite\/fixed time and stabilizes on it, thereby achieving the corresponding consensus tracking. Theoretical analysis reveals that the convergence time of finite-time consensus depends on the system\u2019s initial states, whereas fixed-time consensus is independent of initial conditions but highly influenced by control parameters. Rigorous proofs are provided using graph theory and Lyapunov stability theory, and numerical simulations validate the theoretical findings.<\/jats:p>","DOI":"10.1177\/01423312251352882","type":"journal-article","created":{"date-parts":[[2025,8,26]],"date-time":"2025-08-26T13:24:03Z","timestamp":1756214643000},"page":"2530-2539","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Consensus of second-order nonlinear multi-agent system based on nonsingular terminal sliding mode control with disturbance"],"prefix":"10.1177","volume":"48","author":[{"given":"Mengdan","family":"Zhang","sequence":"first","affiliation":[{"name":"College of Electrical Engineering and Automation, Hubei Normal University, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0914-7546","authenticated-orcid":false,"given":"Jie","family":"Wu","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering and Automation, Hubei Normal University, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9104-699X","authenticated-orcid":false,"given":"Xisheng","family":"Zhan","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering and Automation, Hubei Normal University, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-7272-4301","authenticated-orcid":false,"given":"Lingli","family":"Cheng","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering and Automation, Hubei Normal University, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bo","family":"Wu","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering and Automation, Hubei Normal University, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2025,8,26]]},"reference":[{"key":"e_1_3_2_2_1","doi-asserted-by":"publisher","DOI":"10.3390\/math10071064"},{"key":"e_1_3_2_3_1","doi-asserted-by":"publisher","DOI":"10.3390\/math10101659"},{"key":"e_1_3_2_4_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012997321358"},{"key":"e_1_3_2_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2018.09.068"},{"key":"e_1_3_2_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2023.111296"},{"key":"e_1_3_2_7_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2019.2922740"},{"key":"e_1_3_2_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2021.12.017"},{"key":"e_1_3_2_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2023.10.021"},{"key":"e_1_3_2_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11432-018-9846-y"},{"key":"e_1_3_2_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2006.02.013"},{"key":"e_1_3_2_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2006.08.015"},{"key":"e_1_3_2_13_1","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.2024.3358293"},{"key":"e_1_3_2_14_1","doi-asserted-by":"publisher","DOI":"10.1007\/s40747-021-00334-9"},{"key":"e_1_3_2_15_1","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2024.3402397"},{"key":"e_1_3_2_16_1","doi-asserted-by":"publisher","DOI":"10.1109\/TASE.2024.3445135"},{"key":"e_1_3_2_17_1","doi-asserted-by":"publisher","DOI":"10.1109\/TASE.2024.3384400"},{"key":"e_1_3_2_18_1","doi-asserted-by":"publisher","DOI":"10.1007\/s12555-023-0486-4"},{"key":"e_1_3_2_19_1","doi-asserted-by":"publisher","DOI":"10.3390\/math10081236"},{"key":"e_1_3_2_20_1","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.7205"},{"key":"e_1_3_2_21_1","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2011.2179869"},{"key":"e_1_3_2_22_1","doi-asserted-by":"publisher","DOI":"10.1007\/s12555-020-0283-2"},{"key":"e_1_3_2_23_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2024.120808"},{"key":"e_1_3_2_24_1","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.7957"},{"key":"e_1_3_2_25_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2022.11.035"},{"key":"e_1_3_2_26_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00034-025-03039"},{"issue":"7","key":"e_1_3_2_27_1","first-page":"3164","article-title":"Distributed adaptive finite-time approach for formation\u2013containment control of networked nonlinear systems under directed topology","volume":"29","author":"Wang Y","year":"2017","unstructured":"Wang Y, Song Y, Ren W (2017) Distributed adaptive finite-time approach for formation\u2013containment control of networked nonlinear systems under directed topology. 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