{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T16:08:07Z","timestamp":1760890087859,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2020,6,12]],"date-time":"2020-06-12T00:00:00Z","timestamp":1591920000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100005033","name":"Politechnika Bialostocka","doi-asserted-by":"publisher","award":["S\/WI\/1\/2016"],"award-info":[{"award-number":["S\/WI\/1\/2016"]}],"id":[{"id":"10.13039\/501100005033","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper studies the leader-following consensus problem in continuous-time multi-agent networks with communications\/updates occurring only at random times. The time between two consecutive controller updates is exponentially distributed. Some sufficient conditions are derived to design the control law that ensures the leader-following consensus is asymptotically reached (in the sense of the expected value of a stochastic process). The numerical examples are worked out to demonstrate the effectiveness of our theoretical results.<\/jats:p>","DOI":"10.3390\/e22060650","type":"journal-article","created":{"date-parts":[[2020,6,12]],"date-time":"2020-06-12T05:02:24Z","timestamp":1591938144000},"page":"650","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["On Leader-Following Consensus in Multi-Agent Systems with Discrete Updates at Random Times"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1305-2411","authenticated-orcid":false,"given":"Ricardo","family":"Almeida","sequence":"first","affiliation":[{"name":"Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1111-6730","authenticated-orcid":false,"given":"Ewa","family":"Girejko","sequence":"additional","affiliation":[{"name":"Faculty of Computer Science, Bialystok University of Technology, 15-351 Bia\u0142ystok, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4922-641X","authenticated-orcid":false,"given":"Snezhana","family":"Hristova","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Computer Science, University of Plovdiv Paisii Hilendarski, 4027 Plovdiv, Bulgaria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1309-8583","authenticated-orcid":false,"given":"Agnieszka","family":"Malinowska","sequence":"additional","affiliation":[{"name":"Faculty of Computer Science, Bialystok University of Technology, 15-351 Bia\u0142ystok, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2020,6,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1007\/s11537-007-0647-x","article-title":"On the mathematics of emergence","volume":"2","author":"Cucker","year":"2007","journal-title":"Jpn. 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