The vibration problem and its effects on mechanical systems require special attention because of the consequences that they can cause such as fracture, fatigue or wear. In this context, it is necessary for the design of controllers based on vibration attenuation to reduce these effects. The H ∞ controller synthesis is used to reduce the high variations, ensuring the stability of the controlled system since they work minimizing the resonance peak for the system. Furthermore, in the controller design process is important to consider the operation limits of the actuators to avoid possible saturation problems, Thus, this work presents the synthesis of the state-feedback H ∞ controller design as an optimization problem in the frequency domain in the linear matrix inequalities (LMIs) form to reduce the vibration amplitude avoiding the actuator saturation. The control problem includes an LMI constraint in the H ∞ synthesis to limit the amplitude of the control effort. The designed controller is implemented in an ECP Torsional Plant of 2DOF subject to electrical saturation limits of its actuator where the results obtained are discussed in this work.