{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T14:56:18Z","timestamp":1761663378630,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2015,6,8]],"date-time":"2015-06-08T00:00:00Z","timestamp":1433721600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, the leader-following consensus algorithm, which is accompanied with compensations related to neighboring agents\u2019 delayed states, is constructed for second-order multi-agent systems with communication delay. Using frequency-domain analysis, delay-independent and delay-dependent consensus conditions are obtained for second-order agents respectively to converge to the dynamical leader\u2019s states asymptotically. Simulation illustrates the correctness of the results.<\/jats:p>","DOI":"10.3390\/e17063752","type":"journal-article","created":{"date-parts":[[2015,6,10]],"date-time":"2015-06-10T14:05:45Z","timestamp":1433945145000},"page":"3752-3765","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Delayed-Compensation Algorithm for Second-Order Leader-Following Consensus Seeking under Communication Delay"],"prefix":"10.3390","volume":"17","author":[{"given":"Cheng-Lin","family":"Liu","sequence":"first","affiliation":[{"name":"Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Institute ofAutomation, Jiangnan University,Wuxi 214122, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fei","family":"Liu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Institute ofAutomation, Jiangnan University,Wuxi 214122, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,6,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1520","DOI":"10.1109\/TAC.2004.834113","article-title":"Consensus problems in networks of agents with switching topology and time-delays","volume":"49","author":"Murray","year":"2004","journal-title":"IEEE Trans. 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