Mathematical models of systems are typically incomplete and/or imprecise, and real systems operate in the presence of a variety of external partially unknown or unmeasurable disturbances. Nevertheless, one would like to design high performance control systems in the presence of significant and large uncertainty in the system models and external disturbances. Such designs would be based on quantifying performance objectives in terms of frequency and/or time domain specifications, as well as modeling of uncertain system dynamics. These issues are addressed in this research in the context of linear, nonlinear, and distributed parameter systems. An overall goal is to gain an understanding of the limits of optimal performance of control systems in the presence of significant uncertainty, as well as to develop convergent algorithms for computing these limits and the associated optimally robust controllers.