A current-sensorless PWM-based robust sliding mode controller is proposed for the DC-DC quadratic boost converter, a high-order, bilinear nonminimum phase system that presents major challenges in the design of stabilizing controllers. The development of the controller requires only the measurement of the output voltage. An extended state observer is developed to estimate a lumped uncertainty signal that includes the uncertain load and input voltage and to estimate the derivative of the output voltage. A linear sliding surface is used to derive a simple controller that exhibits excellent features in term of robustness to external disturbances without resorting to the traditional inductor current feedback. Also, a simple procedure to select the controller gains is developed. The robustness of the controller is validated by computer simulations. Future work will be the validation of these results experimentally.