Abstract: For nonlinear differential-algebraic equation systems satisfying linear growth conditions, the problem of output feedback stabilization control is considered in this paper. The design of the state observer is coupled with that of the controller. The proposed observer is non-initialized and linear which makes the observer robust. Based on the backstepping approach, a linear dynamic output compensator is constructed, through which the whole closed-loop systems are asymptotically stable. The simulation results demonstrate the effectiveness of the proposed control scheme.