Attenuation of nonlinear uncertainties using robust control is considered. A system under investigation has a linear nominal part and a nonlinear lumped uncertainty. Robust control is designed using the Lyapunov direct method. It is shown that the proposed control is continuous, guarantees global stability without knowledge of nonlinear dynamics except their size bounding function, and ensures a finite upper bound on the attenuation performance index over an infinite horizon. That is, the proposed control is both robust and optimal. As an application, it is shown that the proposed control can be directly applied to robotic manipulators and many other nonlinear systems.