{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T13:35:05Z","timestamp":1762176905375,"version":"3.37.3"},"reference-count":26,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2016,7,15]],"date-time":"2016-07-15T00:00:00Z","timestamp":1468540800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61374062"],"award-info":[{"award-number":["61374062"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science Foundation of Shandong Province for Distinguished Young Scholars","award":["JQ201419"],"award-info":[{"award-number":["JQ201419"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,3,16]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This article investigates the controllability of path and star graphs under the protocol of second-order neighbours. With identified special control nodes, a sufficient condition is first derived for the controllability of path graph by taking advantage of the protocol of second-order neighbours. Then necessary and sufficient conditions are developed respectively for the single and multiple leaders. Some differences between the protocol of second-order neighbours and first-order neighbours are also presented for path graph. Finally, a necessary and sufficient condition is proposed for the controllability of star graph by taking advantage of the protocol of second-order neighbours.<\/jats:p>","DOI":"10.1093\/imamci\/dnw013","type":"journal-article","created":{"date-parts":[[2016,7,16]],"date-time":"2016-07-16T02:49:24Z","timestamp":1468637364000},"page":"1-14","source":"Crossref","is-referenced-by-count":27,"title":["Necessary and sufficient conditions for multi-agent controllability of path and star topologies by exploring the information of second-order neighbours"],"prefix":"10.1093","volume":"38","author":[{"given":"Yongcui","family":"Chao","sequence":"first","affiliation":[{"name":"College of Automation Engineering, Qingdao University, Qingdao 266071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhijian","family":"Ji","sequence":"additional","affiliation":[{"name":"College of Automation Engineering, Qingdao University, Qingdao 266071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2016,7,15]]},"reference":[{"key":"2021021910174260300_B1","doi-asserted-by":"crossref","first-page":"1366","DOI":"10.1007\/s12555-013-0374-4","article-title":"A controllability synthesis problem for dynamic multi-agent systems with linear high-order protocol","volume":"12","author":"Cai","year":"2014","journal-title":"Int. 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