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Due to the piecewise time-varying characteristics of system matrix, it is challenging to design an appropriate controller to stabilize the error state within each piecewise time period. To overcome this difficulty, a piecewise time-varying Lyapunov function (PTVLF) approach is proposed to analyze the piecewise time-varying systems. Then, a useful lemma guaranteeing the negative definiteness of matrix polynomials is first derived, which is utilized to prove the negative definiteness of the derivative for the PTVLF. Based on this, a novel controller with time-varying gain is presented to stabilize the error state within each piecewise time period. Then, by selecting the dwell time of each topology larger than a positive threshold, the overall consensus of such systems is guaranteed. Finally, a numerical simulation is shown to illustrate the theoretical results.<\/jats:p>","DOI":"10.1177\/01423312221085786","type":"journal-article","created":{"date-parts":[[2022,4,8]],"date-time":"2022-04-08T08:25:18Z","timestamp":1649406318000},"page":"2522-2531","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":13,"title":["Consensus of piecewise time-varying multi-agent systems with switching topologies"],"prefix":"10.1177","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9743-7457","authenticated-orcid":false,"given":"Jian","family":"Sun","sequence":"first","affiliation":[{"name":"Marine Electrical Engineering College, Dalian Maritime University, China"}]},{"given":"Chen","family":"Guo","sequence":"additional","affiliation":[{"name":"Marine Electrical Engineering College, Dalian Maritime University, China"}]},{"given":"Lei","family":"Liu","sequence":"additional","affiliation":[{"name":"College 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