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Using an incidence matrix, the consensus problem of delayed multi-agent systems (time-varying input delays) with relative state saturation is converted into the stability problem of edge dynamics on the closed sets. Then, a new linear control protocol is designed using a saturation function that guarantees stability for all agents under relative state saturation constraints. With the appropriate Lyapunov\u2013Krasovskii functional definition, sufficient conditions are created for the consensus of the agents. Meanwhile, the relative state saturations do not happen. Also, the agents track the leader\u2019s path well, while bounded delays can be time-varying and arbitrarily fast. This consensus and stability are achieved by maintaining graph connectivity. Finally, the correctness of the above content is confirmed by simulating a practical example.<\/jats:p>","DOI":"10.1177\/01423312231162970","type":"journal-article","created":{"date-parts":[[2023,4,21]],"date-time":"2023-04-21T03:05:44Z","timestamp":1682046344000},"page":"2554-2563","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":2,"title":["Consensus tracking control for time-varying delayed linear multi-agent systems under relative state saturation constraints"],"prefix":"10.1177","volume":"47","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0147-5599","authenticated-orcid":false,"given":"Javad","family":"Zanganeh","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad (FUM), Mashhad, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Seyed Kamal","family":"Hosseini Sani","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad (FUM), Mashhad, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6689-9176","authenticated-orcid":false,"given":"Naser","family":"Pariz","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad (FUM), Mashhad, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2023,4,21]]},"reference":[{"key":"e_1_3_2_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2014.10.047"},{"key":"e_1_3_2_3_1","volume-title":"Robust Multivariable Flight Control","author":"Adams RJ","year":"2012","unstructured":"Adams RJ, Buffington JM, Sparks AG, et al. 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