A general methodology has been developed for the design of a robust control law for a family of lightly damped second order problems. In this research effort, the passivity approach has been extended to systems having non-collocated input/output pairs by introducing an observer that incorporates the nominal dynamical model of the plant. The developed passive observer-based control law emulates numerous dynamic vibration absorbers which are tuned to a targeted frequency using classical methods and the tuning ratios are time-invariant. However, the uniqueness of this approach is that the damping parameters of the emulated absorbers are continuously varied by means of a fuzzy logic control algorithm to provide near minimum-time suppression of vibration. The developed approach is applied to both several benchmarks in the field of structural dynamics as well as experiments using piezo-ceramic sensors and actuators. Results show that this methodology provides stability and performance robustness on the one hand as well as requiring relatively low amount of actuation authority for desired nominal plant closeloop behavior.