The　problems　of　feedback　dissipativity　and　stabilization　of　switched　positive　systems　are　investigated　via　the　co-design　of　both　the　combined　switching　strategy　and　the　state　feedback　control.　In　particular,　the　proposed　technique　guarantees　a　minimal　dwell　time　between　the　adjacent　switching　even　when　all　subsystems　are　not　dissipative.　The　time-varying　multiple　linear　co-positive　storage　functions　are　first　adopted　and　sufficient　conditions　of　rendering　the　considered　system　to　be　dissipative　are　also　established.　Moreover,　stability　is　obtained　when　the　multiple　linear　supply　rates　are　non-positive,　and　asymptotic　stability　is　further　achieved　under　certain　redesigned　controller　and　the　detectivity　property　of　all　subsystems.　Finally,　simulation　studies　verify　that　the　proposed　control　scheme　is　valid.