There are many reasons to use feedback control. As we have seen earlier, with the help of an appropriately designed feedback controller we can reduce the effect of noise and disturbances, and we can improve the tracking of command signals. Another very important use for feedback control is the reduction of the effects of plant uncertainty. The mathematical models that we use to describe the plant dynamics are almost never perfect. A feedback controller can be designed so as to maintain stability of the closed-loop and an acceptable level of performance in the presence of uncertainties in the plant description, i.e., so as to achieve robust stability and robust performance respectively.
For the study of robust stability and robust performance, we assume that the dynamics of the actual plant are represented by a transfer function that belongs to some uncertainty set \(\Omega\). We begin by giving mathematical descriptions of two possible uncertainty sets. Many other descriptions exist, and may be treated by methods similar to those we present for these particular types of uncertainty sets.