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In this paper, we study the global robust output regulation problem for a class of multivariable nonlinear systems. The problem is first converted into a stabilization problem of an augmented system composed of the original plant and an internal model. The augmented system is a two-input system containing both dynamic uncertainty and time-varying static uncertainty. By decomposing the two-input control problem into two single-input control problems, we can solve the problem via a recursive approach utilizing the changing supply function technique. Finally, the theoretical result is applied to the speed tracking control and load torque disturbance rejection problem of a surface-mounted PM synchronous motor.