It has been shown that shunting electromagnetic devices with electrical networks can be used to damp vibrations. These absorbers have however limitations that restrict the control performance, i.e., the total damping of the system and robustness versus parameter variations. On the other hand, the electromagnetic devices are widely used in active control techniques as an actuator. The major difficulty that arises in practical implementation of these techniques is the power consumption required for conditioners and control units. In this study, robust hybrid control system is designed to combine the passive electromagnetic shunt damper with an active control in order to improve the performance with low power consumption. Two different active control laws, based on an active voltage source and an active current source, are proposed and compared. The control law of the active voltage source is the direct velocity feedback. However, the control law of the active current source is a revisited direct velocity feedback. The method of maximum damping, i.e., maximizing the exponential time-decay rate of the response subjected to the external impulse forcing function, is employed to optimize the parameters of the passive and the hybrid control systems. The advantage of using the hybrid control configuration in comparison with purely active control system is also investigated in terms of the power consumption. Besides these assets, it is demonstrated that the hybrid control system can tolerate a much higher level of uncertainty than the purely passive control systems.