This chapter intends to briefly review the optimal and robust control. H 2 and H ∞norms and their calculation are first introduced since they are two commonly used measures of performance specifications of a control system. What follow are the H 2 and H ∞ control problems and controller design via a linear matrix inequality approach. Robust control of systems with multiplicative uncertainty and additive uncertainty, and the parametrization of all stable controllers, i.e., the so-called Youla parametrization, will be investigated. Moreover, performance limitation of a feedback control system is discussed, which is necessary to help understand the vibration control schemes in the later chapters.