This paper presents a control technique for a boost converter that is connected to a power source via an LC input filter in a continuous conduction mode. The proposed method employs the Lyapunov stability criterion to determine the switching command that guarantees system stability. An estimator is introduced to track the load resistance and losses of the system in real-time. Our control strategy regulates all state variables of the system and additional state variables in the estimator concurrently. Additionally, the start-up transient response is considered in the control algorithm. Finally, experimental results are provided to validate the effectiveness of the proposed control method.