This paper presents a feasibility study for the vibration control of the SILEX optical payload installed on the European ARTEMIS advanced telecommunication satellite. Due to its stringent pointing requirements (being approximately a few microradiants) the payload is particularly sensitive to the transmitted microvibrational disturbances. The vibration suppression problem has been addressed using piezoceramic strain actuators bonded to the payload support structure and designing a high control authority linear quadratic compensator. The plant mathematical model was obtained through a NASTRAN finite element modeling of the payload structure equipped with the surface bonded piezoceramic strain actuators. This high order evaluation model has successively been reduced to a lower order design model using static condensation (Guyan) and modal reduction techniques. Different criteria have been applied in order to check for the controllability of the system. The LQR compensator design was based on the minimization of a quadratic performance index of state and control vectors which included the output behavior. A comparison between the open and closed loop system behavior was carried out for different disturbance inputs and different control weights.