Inerter is a device that generates a force proportional to the relative acceleration between its two terminals. It has recently been shown that this unusual property can offer interesting advancements and performance in the realm of vibration isolation or dynamic absorbers. However, the main developments have encountered difficulties in mechanical implementation (utilizing rotating discs and gears) or achieving high-frequency efficiency. The present study proposes to synthesize actively the dynamical behavior of an inerter in order to overcome these constraints. To address the stability issue, collocated voice coils are employed as sensors and actuators at the interface of the moving masses of the device. In a case study of a hybrid tuned vibration absorber, a first experimental demonstration illustrates the feasibility of such a concept.