Regional Pole Placement

In conventional modern control theory, as the model uncertainty is not taken into consideration, the so-called pole placement is to place the poles to fixed points in the complex plane. In addition, from the viewpoint of robust performance, the response quality of the closed-loop system is guaranteed if the closed-loop poles can be locked in a prescribed region. This chapter discusses this issue for the nominal system and then extends to the regional pole placement of uncertain systems. It considers how to place the system poles so as to achieve a satisfactory transient response. The chapter also considers a second-order system with distinct eigen values and discusses how to design a feedback controller to place the poles of closed-loop system in a specified LMI region. It analyzes the condition for all poles of a parametric system being placed in a designated LMI region.