An analysis is presented on the use of a proof-mass actuator as a regenerative force actuator for the mitigation of earthquake disturbances in civil structures. A proof-mass actuator is a machine which accelerates a mass along a linear path. Such actuators can facilitate two-way power flow. In regenerative force actuation, a bi- directional power-electronic drive is used to facilitate power flow both to and from the proof-mass actuator power supply. With proper control system design, this makes it possible to suppress a disturbance on a structure using mostly energy extracted from the disturbance itself, rather than from an external power source. In this study, three main objectives are accomplished. First, a new performance measure, called the "required energy capacity," is proposed as an assessment of the minimum size of the electric power supply necessary to facilitate the power flow required of the closed-loop system for a given disturbance. The relationship between the required energy capacity and the linear control system design, which is based on positive position feedback concepts, is developed. The dependency of the required energy capacity on hybrid realizations of the control law are discussed, and hybrid designs are found which minimize this quantity for specific disturbance characteristics. As the second objective, system identification and robust estimation methods are used to develop a stochastic approach to the performance assessment of structural control systems, which evaluates the average worst-case performance for all earthquakes "similar" to an actual data record. This technique is used to evaluate the required energy capacity for a control system design. In the third objective, a way is found to design a battery capacity which takes into account the velocity rating of the proof-mass actuator. Upon sizing this battery, two nonlinear controllers are proposed which automatically regulate the power flow in the closed-loop system to accommodate a power supply with a finite energy capacity, regardless of the disturbance size. Both controllers are based on a linear control system design. One includes a nonlinearity which limits power flow out of the battery supply. The other includes a nonlinearity which limits the magnitude of the proof-mass velocity. The latter of these is shown to yield superior performance. / Master of Science