This paper introduces a general framework for control design which can be used to solve several open problems in robust and optimal control. These include systems subject to independently norm-bounded disturbances, robust stability for systems subject to "element by element" bounded structured uncertainty, certain classes of robust performance problems, and systems subject to deterministic white noise disturbances, This is achieved by combining concepts such as H-infinity optimization, linear matrix inequalities, and integral quadratic constraints, Necessary and sufficient conditions for the general problem to have a solution are in terms of a computationally attractive finite-dimensional linear matrix inequality.