In　this　paper,　a　family　of　amplitude　limited　controllers　and　a　hysteresis　switching　paradigm,　for　switched　positive　systems　with　time-varying　delays,　are　simultaneously　determined　to　achieve　strict　(q,　r)-alpha-dissipativity.　The　concept　of　strictly　(q,　r)-alpha-dissipative,　induced　by　linear-type　dissipative　inequalities,　is　introduced.　The　main　feature　of　the　presented　method　lies　in　two　aspects.　The　first　one　is　that　the　magnitude　of　controller　discontinuities,　at　the　occurrence　of　switching,　is　here　restricted.　The　other　one　is　that　the　high　switching　frequency　is　refrained　commonly　the　appearance　of　in　state-dependent　switching　schemes.　Moreover,　dissipativity　analysis　as　well　as　feedback　dissipativity　are　taken　into　account.　Novel　criteria　are　derived　for　the　considered　systems　to　be　dissipativity　by　resorting　to　multi-linear　copositive　storage　functionals.　Eventually,　the　validity　and　superiority　of　the　presented　control　strategy　are　demonstrated　through　two　illustrative　examples.