This paper considers the robust observer design problem for linear dynamic systems subject to the interference of external disturbances. For such systems, the state estimate from the conventional Luenberger is normally biased with respect to the true system state. To remedy this situation, this paper proposes a new structure for robust observers. With this new structure, the robust observer design problem is skillfully transformed into the well-known disturbance rejection control problem. The H-infinity optimal control design technique can then be applied to shape the proposed robust observer in the frequency domain. The proposed robust observer is a joint state and disturbance observer, which simultaneously estimates both the system state and unknown disturbances, and can be applied to non-minimum-phase systems.