{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T15:39:48Z","timestamp":1769182788460,"version":"3.49.0"},"reference-count":38,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,10,27]],"date-time":"2021-10-27T00:00:00Z","timestamp":1635292800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62003289 , U1703262"],"award-info":[{"award-number":["62003289 , U1703262"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Tianshan Youth Program","award":["2018Q068"],"award-info":[{"award-number":["2018Q068"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, the leader-following consensus problem of first-order nonlinear multi-agent systems (FONMASs) with external disturbances is studied. Firstly, a novel distributed fixed-time sliding mode manifold is designed and a new static event-triggered protocol over general directed graph is proposed which can well suppress the external disturbances and make the FONMASs achieve leader-following consensus in fixed-time. Based on fixed-time stability theory and inequality technique, the conditions to be satisfied by the control parameters are obtained and the Zeno behavior can be avoided. In addition, we improve the proposed protocol and propose a new event-triggering strategy for the FONMASs with multiple leaders. The systems can reach the sliding mode surface and achieve containment control in fixed-time if the control parameters are designed carefully. Finally, several numerical simulations are given to show the effectiveness of the proposed protocols.<\/jats:p>","DOI":"10.3390\/e23111412","type":"journal-article","created":{"date-parts":[[2021,10,27]],"date-time":"2021-10-27T22:00:23Z","timestamp":1635372023000},"page":"1412","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Event-Triggered Fixed-Time Integral Sliding Mode Control for Nonlinear Multi-Agent Systems with Disturbances"],"prefix":"10.3390","volume":"23","author":[{"given":"Xue","family":"Li","sequence":"first","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8073-057X","authenticated-orcid":false,"given":"Zhiyong","family":"Yu","sequence":"additional","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China"}]},{"given":"Haijun","family":"Jiang","sequence":"additional","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1113","DOI":"10.1049\/iet-cta.2019.0210","article-title":"Distributed regular polygon formation control and obstacle avoidance for non-holonomic wheeled mobile robots with directed communication topology","volume":"14","author":"Wang","year":"2020","journal-title":"IET Control. 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