This paper presents an observer-based friction compensation design for a class of frictional systems guaranteeing global exponential stability of the closed-loop system in the absence of velocity measurements. The friction compensation scheme allows a fairly general discontinuous friction model that is able to describe stiction and the Stribeck effect, and which can fit experimentally obtained velocity-friction maps. The design method is based on passivity theory. It only involves well-known linear design criteria: strictly positive real (SPR) and Hurwitz conditions, and it preserves the separation and the certainty equivalence principles. The effectiveness of the design method is tested on an experimental setup.