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The objective of this paper is to detail an analytical method allowing the large signal stability analysis of an electric system constituted by an input filter connected to an actuator (inverter - permanent magnet synchronous motor or induction motor). The proposed approach supposes that a nonlinear control is used to drive the actuators. The studied control allows decoupling the control of torque from the variations of the DC-link voltage and those for any operating point. In many studies, the design of the dc-link capacitance is based on a first order modeling of the system and is realized to ensure only the asymptotic stability around the operating point. The stability is then proved around the operating point. Nevertheless the behavior of the system in case of large disturbances is unknown. In fact the state trajectory goes away from the operating point and behavior of the state trajectory is not foreseen by the modeling. If the state trajectory stays in its attraction region, then it will converge towards the operating point. The present work explains a method based on the takagi sugeno theorem which generates a quadratic lyapunov function which allows the determination of an attraction domain for a given operating point. The knowledge of such a set allows estimating the robustness properties of the control and provides a tool to design the dc-link capacitance value thanks to an estimation of the attraction domain.