Introduction to Time-Delay Systems

We begin this chapter by presenting a number of practical examples of time-delay systems. This should give the reader a glimpse into how widely time delays may occur in practice. To make the presentation more accessible, we then analyze a simple time-delay system, which illustrates some of the important concepts in a concrete manner. This analysis sets the stage for a formal introduction to functional differential equations as a representation of time-delay systems, and to such stability analysis tools as the LyapunovKrasovskii Theorem and Razumikhin Theorem. Linear delay systems are discussed in greater length with frequency domain descriptions. The chapter is concluded with a brief outline of subsequent content.