Active base isolation has been studied in the last few decades to improve the control performance of base isolation. As a two-degree-of-freedom active disturbance-rejection method, the equivalent-input-disturbance (EID) approach shows its validity for structural control. It uses a state observer to estimate the effect of disturbances on a control input channel. However, since the model of a base-isolated building has high degrees-of-freedom, the resulting control system has a high order. Thus, the use of a full-order state observer results in the complexity of a control-system implementation. To solve this problem, this paper presents an EID control system that uses a reduced-order state observer (ROSO) to reduce the expense of control-system implementation and ensure system reliability. First, the condition of using an ROSO in an EID control system is derived, and the configuration of an ROSO-based EID control system is presented. Next, the concept of perfect regulation is used to design the gain of the state observer. A stability condition of the system with prescribed control performance is derived in the form of a linear matrix inequality (LMI) that is used to design the gain of the state feedback. Finally, the seismic control of a base-isolated building demonstrates the validity of the method.