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First, we design a DETS that introduces an internal dynamic variable (IDV) into the event-triggered condition, which can improve data transmission efficiency and decrease the cost of the system operation by expanding the interevent intervals. Second, we establish a state observer based on the DETS and further construct an observer-based state feedback controller. It is worth noting that asynchronous switching may occur between the subsystems and the controllers under the DETS. Third, by utilizing novel Lyapunov-like functions (LLFs) with IDV and the signal-combining approach, sufficient conditions to ensure the [Formula: see text] performance of the closed-loop system are presented. Moreover, we verify that Zeno phenomenon does not exist. Finally, the effectiveness of the proposed method is verified by two examples.<\/jats:p>","DOI":"10.1177\/01423312241234386","type":"journal-article","created":{"date-parts":[[2024,4,1]],"date-time":"2024-04-01T07:19:01Z","timestamp":1711955941000},"page":"3040-3052","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":2,"title":["Dynamic event-triggered\n                    <i>H<\/i>\n                    <sub>\u221e<\/sub>\n                    control for switched linear systems with internal dynamic variable"],"prefix":"10.1177","volume":"46","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9179-9297","authenticated-orcid":false,"given":"Yiman","family":"Yu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Shaanxi Normal University, P.R. 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