This paper presents a new control strategy for a quadratic boost converter used in solar energy system. The proposed control strategy is based on Lyapunov theory that provides the stability of the converter considered as a switched affine system, it also allows a maximum power extraction by fixing the operating point near of the maximum power point (MPP). The voltage is fixed at a constant value VMPP if the irradiation varies in a small interval, or the derivative of the power with respect to the voltage is fixed at zero. The system doesn't contain any maximum power point tracking (MPPT) controller, the MPPT is integrated in the control strategy. The simulation results have proved the robustness of the proposed control strategy and the comparison with a classic controller has shown its advantage, the output is smoother and the extracted power is m.aximum without using a MPPT controller.