In order to study the lateral instability problem caused by vibration bifurcation and lateral disturbance in the train–bridge interaction system during the operation of maglev trains, a nonlinear time-varying train–bridge interaction model was established using the Hamiltonian variational principle, and the feedback gain stabilization area and its bifurcation threshold characteristics were quantitatively analyzed based on the Floquet theory. The influences of factors such as vehicle speed, steady-state current, and bridge parameters on the stable range of feedback gain of the guidance system were discussed. From the perspective of full-value stability domain of the feedback gains, the control strategy for suppressing the effect of wind-induced lateral loads on the vibration characteristics of the system was discussed. Research shows that appropriately increasing the displacement feedback gain and integral feedback gain can effectively suppress the offset of the center position of the guidance gap vibration caused by crosswind. However, their values must be strictly limited within their stable threshold; otherwise, it may induce system vibration bifurcation. In addition, increasing the speed feedback gain or current feedback gain can effectively suppress the lateral vibration bifurcation phenomenon during the operation of maglev trains.
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