Voltage Control of Boost Converters: Feasibility Guarantees*

This paper deals with the design of a novel static nonlinear controller to regulate the voltage of boost converters while fulfilling physical constraints; at any time instant, the states need to be positive, and the duty cycle of the converter takes an admissible value between zero and one. The proposed controller is based on a shifted Lyapunov function and asymptotically stabilizes the desired equilibrium point of the closed-loop system as long as the voltage and current are positive at any time instant. To guarantee positivity, we derive a necessary and sufficient condition for identifying a feasible level set that is contained in the positive orthant and is positively invariant. Next, to ensure a feasible implementation and operation of the proposed controller, we derive a necessary and sufficient condition on the controller feedback gain to ensure that the converter duty cycle takes admissible values between zero and one. Finally, the most significant theoretical results are validated in simulation.