The robust decentralized connective stabilization problem based on output feedback for a class of power systems with expanding construction, which is constituted by adding new subsystems one after another on the original construction, is considered in this paper. The robust decentralized connective stabilization problem for the power system is how to design the local control law of the new subsystem based on not changing the decentralized control laws of original construction, so that both the subsystem and the resultant expanded power system are connective stable. The sufficient condition of the robust decentralized connective stabilization based on output feedback for the expanding construction of the power systems is obtained by taking Lyapunov theory and LMI approach. The design method of the robust decentralized output feedback controller of the expanding construction is given. The method is applied to AGC control design of a class of power systems with expanding construction, and the simulation results show the effectiveness of presented method.