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Firstly, the communication topology of a swarm system is depicted by a directed graph with a spanning tree, where the communication channels from the leader to followers are directional and the communication channels among followers are bidirectional, and a new formation tracking protocol with an energy integral term and a given upper bound is proposed to achieve formation tracking with the limited energy. Then, sufficient conditions for time-varying formation tracking design and analysis with the limited energy are presented, respectively, which include two\/three linear matrix inequality constraints associated with the maximum and minimum nonzero eigenvalues of the Laplacian matrix of a communication topology. Especially, time-invariant formation tracking criteria are further deduced. Finally, two numerical examples are revealed to verify main theoretical conclusions.<\/jats:p>","DOI":"10.1155\/2020\/6678190","type":"journal-article","created":{"date-parts":[[2020,10,29]],"date-time":"2020-10-29T03:05:12Z","timestamp":1603940712000},"page":"1-14","source":"Crossref","is-referenced-by-count":4,"title":["Formation Tracking for High-Order Time-Invariant Swarm Systems with Limited Energy and Fixed Topologies"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5053-2342","authenticated-orcid":true,"given":"Jianye","family":"Yang","sequence":"first","affiliation":[{"name":"School of Science, Xijing University, Xi\u2019an 710123, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7860-9604","authenticated-orcid":true,"given":"Cheng","family":"Wang","sequence":"additional","affiliation":[{"name":"High-Tech Institute of Xi\u2019an, Xi\u2019an 710025, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5170-0419","authenticated-orcid":true,"given":"Hongtao","family":"Dang","sequence":"additional","affiliation":[{"name":"School of Science, Xijing University, Xi\u2019an 710123, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8374-0618","authenticated-orcid":true,"given":"Xinzhong","family":"Han","sequence":"additional","affiliation":[{"name":"Beijing BlueVision Technology Limited Company, Beijing 100070, China"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1109\/tac.2005.864190"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1109\/tase.2019.2961258"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1109\/tsmc.2018.2852277"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1155\/2018\/7831317"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1109\/TCNS.2016.2641800"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2019.2963172"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1109\/tsmc.2018.2883907"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1109\/tcsi.2020.2975383"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1109\/tcns.2015.2489338"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1109\/access.2019.2896978"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2007.09.019"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1109\/tac.2012.2209269"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1109\/tcyb.2018.2875559"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1049\/iet-cta:20050401"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2020.2972403"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1007\/s11424-018-7265-y"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1155\/2020\/7685460"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1109\/tac.2004.834433"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2016.2610140"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-014-1731-4"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1109\/tac.2014.2303213"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1016\/j.robot.2014.07.005"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2016.06.024"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2009.07.012"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1109\/tie.2016.2593656"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1109\/tac.2017.2673411"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.4051"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.4941"},{"key":"29","doi-asserted-by":"publisher","DOI":"10.1109\/tsmc.2018.2883516"},{"key":"30","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4613-0163-9","volume-title":"Algebraic Graph Theory","author":"C. 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