## 1 Introduction  
### Motivations  
Vibrations in mechanical systems, such as mechanisms and structures, arise due to their low stiffness-to-mass ratio and light damping. In the case of the harmonic excitation of disturbance forces, an effective approach to absorb vibration is creating antiresonances in the system frequency response. Indeed, when excited at the antiresonance frequencies, the system experiences no (or very small) steady-state vibration in some particular coordinates. One of the first methods, and probably the most famous one, addressing vibration absorption through antiresonance assignment is the seminal work proposed by [PERSON] in 1911 through his patent [1], where the so-called Tuned Mass Damper (TMD) has been introduced. Thereafter, several approaches and techniques to antiresonance assignment have been developed in the literature and in practical application too. Basically, these methods can be grouped into passive and active. The former consists in the structural modification of the system matrices **M**, **C**, **K**, either by adding degrees-of-freedom (DOFs) or by just modifying the existing ones, without any external power source. In contrast, the latter (together with semi-active approaches) exploit active devices like actuators and sensors, i.e., requiring an external power source. Passive approaches are usually more efficient under an energy point of view and also cheaper, since no external power, actuators, sensors and controllers are needed. The number of antiresonances to be assigned must be matched by the rank of the modification [2,3] if constraints on the feasible modifications are neglected. In practice, the number of assignable antiresonances is usually smaller than the rank of the modification due to constraints on the feasible modifications of parameters that are usually assumed to avoid bulky modifications to the physical parameters. In term of performances, the system is guaranteed to remain stable due to the symmetric nature of the physical modification [4]. On the other hand, the form of the modification that can be realized physically (described through symmetric, positive-definite or semi positive-definite matrices with an imposed pattern of non-zero terms) is restrictive. Another important feature to consider is that passive techniques have no capability to adapt to changing conditions, that can be tackled just through robustness, and hence their effectiveness can be severely reduced. These limitations have been motivating the research on antiresonance assignment through active vibration control, where the role of the spring-mass systems is replaced by forces actively exerted by one or more actuators based on sensor measurements. The features of active approaches to antiresonance assignment are complementary to those of passive approaches. Active control enlarges the achievable performances by suitably choosing the actuator and sensor placements and the control logic: for example, the active control can emulate asymmetric modifications of mass and stiffness matrices. By developing adaptive control logic, active approaches can quickly adapt their response to changing environmental conditions and can be targeted to different excitations with different frequencies, thus being effective in a wide frequency range. However, stability is not always ensured; reduced actuator and sensor bandwidths or delayed response, as well as a bad tuning of the controller gains, may degrade the performances and cause instability. On the other hand, the actuators should be, obviously, properly sized in terms of feasible force, displacement, and speed. Additionally, active approaches are more difficult to implement and require significant control efforts, both in term of forces, power, and energy.