The　stability　problem　of　switched　positive　systems　(SPSs)　with　unstable　subsystems　is　studied.　Two　kinds　of　SPSs　are　studied,　of　which　the　subsystems　are　partially　unstable　and　all　unstable.　For　stability　analysis,　a　delicate　time-scale　multivariate　linear　copositive　Lyapunov　function　(TSMLCLF)　is　established.　The　constructed　Lyapunov　function　changes　with　time　in　some　designed　time　intervals,　and　is　time-invariant　outside　these　time　intervals.　Fast　and　slow　mode-dependent　average　dwell　time　(MDADT)　techniques　are　used　to　solve　stability　problem　with　unstable　and　stable　subsystems,　respectively.　Moreover,　some　improved　conditions　to　ensure　the　stability　of　the　system　are　proposed.　Finally,　two　examples　are　given　to　verify　the　effectiveness　of　our　presented　method.　©　2021　IEEE