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Abstract This paper investigates a bumpless transfer control problem for uncertain switched positive linear time‐delay systems (SPLTDSs) with discrete and distributed delays. The innovation of this study is to develop a linear feedback controller and design a switching law that ensures lower controller signal bumps due to the switches of the SPLTDSs and also guarantee the L1–gain performance of the system. To this end, a bumpless transfer performance is proposed, and stabilisation constraints for SPLTDSs with synchronous switching are developed. Dwell time criteria are utilised in the stability analysis. Also, the results are improved to cover the uncertain SPLTDSs with interval or polytopic uncertainties. Then, asynchronous switching is considered, and the proposed method is extended to deals with asynchronous switching mode. Asynchronous switching means switches of the controller have lagged behind the subsystem switches. All the stability conditions are derived by multiple co‐positive Lyapunov–Krasovskii functional for synchronous and asynchronous switching conditions. At last, two numerical examples are presented to show the effectiveness of the proposed method compared with the leading existing solutions.