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) -α-dissipativity. The concept of strictly (q,r)-α-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.