In this article, we propose a PI passivity-based controller, applicable to a large class of switched power converters, that ensures global state regulation to a desired equilibrium point. A solution to this problem requires full state-feedback, which makes it practically unfeasible. To overcome this limitation we construct a state observer that is implementable with measurements that are available in practical applications. The observer reconstructs the state in finite-time, ensuring global convergence of the PI. An adaptive version of the observer, where some parameters of the converter are estimated, is also proposed. The excitation requirement for the observer is very weak and is satisfied in normal operation of the converters. Realistic simulation results illustrate the excellent performance and robustness vis-Ć -vis noise and parameter uncertainty of the proposed output-feedback PI.