This work aims to study a cascade of two BOOST converters. First, a non- linear model of the whole controlled system is developed. Then, a robust non-linear controller of currents is synthesized using a backstepping design technique. A formal analysis based on Lyapunov stability and average theory is developed to describe the control currents loops performances. A classical PI controller is used for the voltages loops. The study of the stability of the system will also be discussed. Simulated results are displayed to validate the feasibility and the effectiveness of the proposed strategy.