Geometric Tools for Time-Delay Systems

In this chapter, we introduce the main tools that will be used in the book to deal with nonlinear time-delay systems affected by constant commensurate delays. We will introduce basic notions such as the Extended Lie derivative and the Polynomial Lie Bracket (Califano et al. 2011a; Califano and Moog 2017) which generalize to the time-delay context the standard definitions of Lie derivative and Lie Bracket used to deal with nonlinear systems. We will finally show how changes of coordinates and feedback laws act on the class of systems considered.