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This paper investigates the problem of regulating the output voltage of a battery-driven boost converter, where the load is uncertain or changes within a certain range. The battery is modeled with a second order circuit with two capacitors. A state-space approach is developed for estimating the parameters of the battery. By using the state-space averaging method, the open-loop system for regulating the output voltage is described as a sixth order differential equation with a bilinear term and input constraints. A simple saturated state feedback is designed by solving some optimization problem with linear matrix inequality constraints. The optimized controller is very close to an integrator feedback. Using the newly developed Lyapunov method, we analyze the stability and regulation of the closed-loop bilinear system including the battery dynamics. Computation shows that both the optimized state feedback and the integrator feedback can achieve practically global regulation in the presence of uncertain load and uncertain battery voltage. The results are validated by experimental systems. The effect of discontinuous conduction mode on transient response is discussed via simulation and experiment.