Abstract: To deal with the structure jumping problem resulting from elastic load force and external load force jumping in different working conditions, an adaptive backstepping control method of multi-model switching was presented based on the common Lyapunov function method and the adaptive backstepping method. This approach combines the features of adaptive backstepping control and the design requirements of a common Lyapunov function, and the adaptive controller for every sub-system and the parameter adaptive estimators for the uncertainty upper bound are designed by backstepping control, then taking the Lyapunov function designed by backstepping as a common Lyapunov function to ensure that the system is asymptotically stable under arbitrary switching. It is easy to select the common Lyapunov function by the combination of backstepping and the common Lyapunov function method, and the problem of parameter jumping and parameter slow time-varying existing at the same time is solved. Simulation results demonstrate that the designed controllers can ensure not only good dynamic and static performance for the hydraulic servo position system of a rolling mill, but also good robustness for the system parameter jumping and parameter slow time-varying.