Friction-Induced Vibration and noisE (FIVE) is still a complex and nonlinear physical phenomenon which is characterized by the appearance of instabilities and self-sustained vibrations. This undesirable vibrational phenomenon is encountered in numerous industrial applications and can cause major failures for mechanical systems. One possibility to limit this vibration phenomenon due to the appearance of instabilities is to add a controller on the system. This study proposes to discuss the efficiency but also limitations of an active control design based on full linearization feedback. In order to achieve this goal, a complete study is performed on a phenomenological mechanical system subjected to mono or multi-instabilities in the presence of friction. Transient and self-excited vibrations of the uncontrolled and controlled systems are compared. More specifically, contributions of linear and nonlinear parts in the control vector for different values of friction coefficient are investigated and the influence of the control gain and sensitivity of the controller to the signal-to-noise ratio are undertaken.