This paper presents full-state feedback controller synthesis methods that are robust to inverse additive uncertainty via the Large Gain Theorem. In particular, the controller synthesis methods can account for unstable uncertainties. Controllers are designed to either maximize robustness or maximize performance while satisfying a linear matrix inequality (LMI) that enforces a sufficient condition on the minimum gain of the closed-loop system. The Large Gain Theorem is used to prove the robust input-output stability of the system subject to inverse additive uncertainty. A numerical example is provided to illustrate the proposed controller design methods.