This paper considers the problem of global output feedback control for a class of nonlinear systems with inverse dynamics. The main contribution of paper is that: For the inverse dynamics with uncertain ISS/iISS supply rates, and the systems being disturbed by L2 noises, we construct a reduced-order observer-based output feedback controller, which drives the output of system to zero and maintain other closed-loop signals bounded. Finally, a simulation example shows the effectiveness of the control scheme.