ABSTRACT
This chapter reviews the optimal and robust control. H2 and H8 norms and their calculation are first introduced since they are two commonly used measures of performance specifications of a control system. Robust control of systems with multiplicative uncertainty and additive uncertainty, and the parametrization of all stable controllers, that is, the so-called Youla parametrization. A control engineering interpretation of the infinity norm of a scalar transfer function is the distance in the complex plane from the origin to the farthest point on the Nyquist plot, and it also appears as the peak value on the magnitude plot. The optimal H8 control problem is to find an internally stabilizing controller such that the closed-loop system is minimized. The parametrization for all stabilizing controllers is known as Youla parametrization. In the classical feedback control theory, it has been common to express design goals in terms of the shape of the open-loop transfer function.
