This　research　concerns　stability　and　l(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　l(1)-gain　performance.　Finally,　the　proposed　theoretical　techniques　are　verified　through　the　simulation　example.