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We study the influence of time-varying orthogonal optical injection on polarization switching (PS) of vertical-cavity surface-emitting lasers (VCSELs). Three cases are considered: scanning injection strength, and scanning frequency detuning in two different reference ranges. In all the three cases, fast sweep rates make PSs happen at higher (lower) values for upward (downward) scans, and thus enlarge the hysteresis region. Furthermore, types of PS and the emission states of the laser can be controlled, if the scanning parameter and scanning range are chosen properly. Statistical analysis indicates PS for the third case is not so stable as that for the first two cases.