This　research　concerns　stability　and　(Formula　presented.)　-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　(Formula　presented.)　-gain　performance.　Finally,　the　proposed　theoretical　techniques　are　verified　through　the　simulation　example.　©　2022　John　Wiley　&　Sons　Ltd.