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First, by applying weighted orthogonal polynomials, two new integral inequalities are established, which include some existing ones. Second, an event-triggered scheme is presented to save the precious communication resources. After constructing an augmented Lyapunov\u2013Krasovskii functional, a few sufficient conditions are derived to achieve the leader-following event-triggered consensus by utilizing the presented inequalities to manipulate the derivative of the functional. Finally, numerical simulation shows the effectiveness of the proposed method.<\/jats:p>","DOI":"10.1177\/01423312241267036","type":"journal-article","created":{"date-parts":[[2024,8,10]],"date-time":"2024-08-10T01:58:28Z","timestamp":1723255108000},"page":"1138-1153","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Event-triggered leader-following consensus of nonlinear semi-Markovian multi-agent systems via improved integral inequalities"],"prefix":"10.1177","volume":"47","author":[{"given":"Yu","family":"Lu","sequence":"first","affiliation":[{"name":"Department of Mathematics, Dalian Jiaotong University, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4006-5373","authenticated-orcid":false,"given":"Cheng-De","family":"Zheng","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Dalian Jiaotong University, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2024,8,9]]},"reference":[{"key":"e_1_3_3_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.2017.2774841"},{"key":"e_1_3_3_3_1","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2019.2949282"},{"key":"e_1_3_3_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2018.04.054"},{"key":"e_1_3_3_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2014.10.025"},{"key":"e_1_3_3_6_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2016.2601488"},{"key":"e_1_3_3_7_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2017.2789296"},{"key":"e_1_3_3_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-0163-9"},{"key":"e_1_3_3_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2019.11.002"},{"key":"e_1_3_3_10_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2019.2920093"},{"key":"e_1_3_3_11_1","doi-asserted-by":"publisher","DOI":"10.1080\/00207721.2016.1181224"},{"key":"e_1_3_3_12_1","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.2862"},{"key":"e_1_3_3_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2022.02.024"},{"key":"e_1_3_3_14_1","doi-asserted-by":"publisher","DOI":"10.1049\/iet-cta.2009.0346"},{"key":"e_1_3_3_15_1","doi-asserted-by":"publisher","DOI":"10.1155\/2017\/4157256"},{"key":"e_1_3_3_16_1","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2010.2054107"},{"key":"e_1_3_3_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2016.05.070"},{"key":"e_1_3_3_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2015.03.010"},{"key":"e_1_3_3_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2015.01.004"},{"key":"e_1_3_3_20_1","doi-asserted-by":"publisher","DOI":"10.1002\/acs.3245"},{"key":"e_1_3_3_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2015.03.007"},{"key":"e_1_3_3_22_1","doi-asserted-by":"publisher","DOI":"10.1137\/0311017"},{"key":"e_1_3_3_23_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2017.03.032"},{"key":"e_1_3_3_24_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2020.125156"},{"issue":"3","key":"e_1_3_3_25_1","first-page":"1005","article-title":"Generalized","volume":"31","author":"Xin B","year":"2021","unstructured":"Xin B, Zhao D (2021) Generalized H2 control of the linear system with semi-Markov jumps. 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