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Leader-follower network attribute refers to the topology structure and information communication among agents. Coupling input disturbance includes the number of external coupling inputs and the selection of leader nodes. When the leader-follower network attribute is fixed, the selection method of coupling input disturbance is studied for the controllability, and when the coupling input disturbance is known, we derive necessity and sufficiency conditions to determine the controllability. The reliability of theoretical results is verified by numerical examples and model simulation. Besides, the generally perfect controllability is introduced, that is, the system is always controllable regardless of the number and the locations of leaders. In practical engineering applications, the perfectly controllable topology can improve the system fault tolerance and accelerate the commercialization process, which has a profound significance for promoting the modernization process.<\/jats:p>","DOI":"10.1155\/2020\/7685460","type":"journal-article","created":{"date-parts":[[2020,2,28]],"date-time":"2020-02-28T18:34:29Z","timestamp":1582914869000},"page":"1-18","source":"Crossref","is-referenced-by-count":14,"title":["Jordan Form-Based Algebraic Conditions for Controllability of Multiagent Systems under Directed Graphs"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9992-0146","authenticated-orcid":true,"given":"Shuai","family":"Liu","sequence":"first","affiliation":[{"name":"Institute of Complexity Science, College of Automation, Qingdao University, Qingdao 266071, 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