Over one Century of Spectrum Analysis in Delay Systems: An Overview and New Trends in Pole Placement Methods

Pole placement represents a classical method for controlling finite-dimensional linear time-invariant systems, largely covered in the open literature. Basically, it consists of placing the poles of the closed-loop system in some predetermined loci in the complex plane. This paper discusses some of the extensions of this method to linear systems described by delay-differential equations. Among others, the finite spectrum assignment (FSA), the continuous pole placement (CPP) and the partial pole placement (PPP) approaches are presented and illustrated through some simple low-order dynamical systems.