This research concerns stability and ℓ1$$ {\ell}_1 $$‐gain analysis for discrete‐time switched positive systems with time‐varying delay. The switching among subsystems is orchestrated by a state‐dependent switching mechanism. Different from the existing relevant results for discrete‐time switched time‐delay systems with the similar switching framework, an ameliorative switching manner associated with a novel step‐dependent multiple linear copositive Lyapunov–Krasovskii functional (LKF) is established, which eliminates the common constraint in the construction of the conventional LKF. Also, new criteria with less conservativeness are derived for the switched positive time‐delay systems to be asymptotically stable with an ℓ1$$ {\ell}_1 $$‐gain performance. Finally, the proposed theoretical techniques are verified through the simulation example.
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