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This paper presents the stabilization of the input DC voltages of five-level diode-clamped (FLDC) voltage source inverters (VSI). We propose a cascade circuit consisting of a FLDC rectifier a FLDC VSI. First, the different cascade parts and their control strategies are presented. The stability problem of the input DC voltages of the inverter is investigated. To remedy to this problem, two solutions are proposed: the first one uses the linear feedback control algorithm and the second one uses the non-linear control by the Lyapunov technique at the FLDC rectifiers. As an application, the performances of the double star induction machine (DSIM), as fed by the cascade, are observed. The obtained results are full of promise concerning the use of multilevel diode clamped inverters in high voltage/high power applications such as electrical traction.