This　study　focuses　on　stabilization　and　ell-{1}-gain　analysis　problems　for　discrete-time　switched　positive　systems　in　the　presence　of　asynchronous　switching.　The　time-varying　asynchronous　state　feedback　controllers　for　subsystems　are　devised,　where　＇asynchronous＇　indicates　that　the　switching　of　the　controllers　has　a　lag　to　the　switching　of　positive　subsystems.　Based　on　the　dwell　time-dependent　switching　signal,　we　adopt　the　time-varying　multiple　linear　copositive　Lyapunov　function　to　attain　less　conservative　synthesis　conditions　that　ensure　the　positivity,　stability　and　ell-{1}-gain　of　the　closed-loop　system.　All　the　design　conditions　are　cast　in　form　of　linear　vector　inequalities　and　can　be　solved　easily　in　terms　of　linear　programming　tools.　Finally,　the　superiority　of　the　theoretical　results　is　revealed　via　a　simulation　example.　©　2022　Technical　Committee　on　Control　Theory,　Chinese　Association　of　Automation.