Publisher Summary This chapter discusses that the purpose of closed loop control—that is, is to monitor the behavior of a dynamical system by means of appropriate feedback to achieve a prescribed goal. An important characteristic is the stability, or for linear systems, the location of the closed loops poles. These poles determine the qualitative behavior of the system variables. The design of appropriate feedback laws to obtain stability or a preassigned location of the poles and the study of the limitations imposed by constraints on the possible feedback strategies constitute a major research area in control theory. A complete theory exists for pole assignment for linear time invariant systems by means of linear time invariant state feedback and pole assignment for linear time invariant systems by means of linear time invariant dynamic output feedback. The chapter also deals with discrete time systems. The analysis of continuous time systems with time varying elements is technically more complicated. Many of the results obtained for discrete time systems can be formulated as results for continuous time systems with a sample and hold in the feedback loop.