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This article mainly investigates the state‐feedback L1$$ {L}_1 $$ finite‐time control problem for discrete‐time switched positive linear systems with mode‐dependent persistent dwell‐time (MDPDT) switching. The MDPDT switching is more general than the common dwell‐time and average dwell‐time switching because it can perfectly model a type of switched systems with hybrid slow and fast switching properties. Considering the positivity of the system, we adopt multiple linear copositive Lyapunov functions instead of traditional quadratic Lyapunov functions and derive sufficient criteria of finite‐time stability by utilizing the linear programming approach. Then the relationship between the lower bound of such switching signals and parameters of the constructed controllers is found successfully, and a sufficient condition to ensure that the closed‐loop switched system maintains positive and L1$$ {L}_1 $$ finite‐time bounded is proposed. Finally, the efficiency of our developed conclusions is validated by two illustrative examples.