Abstract The Conic Sector Theorem is a powerful input-output stability result that can be used for controller synthesis. This talk will survey existing methods that impose conic requirements while reducing the closed-loop H2-norm to achieve good performance and stability. These will be compared to a new conic design technique that minimizes an upper-bound on the closed-loop H2-norm while imposing constraints to satisfy the conic properties. Numerical results have shown that this method leads to good performance, providing a useful tool for robust and optimal control.