A hybrid Lyapunov control for a flying capacitor multicellular converter is presented. This control law is based on the Port-Hamiltonian (PH) formalism of power converters and allows to enhance load current quality and reduce switching losses. The proposed control is applied to a three-cell multicellular converter. A procedure for selecting the best weighting parameters in the control law according to a performance criterion is presented. The simulation and experimental results indicate the stability of the control for changes in the reference signals. A comparison with a different Lyapunov control technique shows the performance of the proposed solution and the advantage of such a strategy in order to reduce the switching losses.