Linear Time-Invariant Descriptor Systems

In this chapter, we recall some basic concepts concerning linear time-invariant descriptor systems for both continuous-time and discrete-time settings, which will be used subsequently. Descriptor systems offer a powerful tool for system modelling since they allow to describe a system by both dynamic equations and algebraic constraints. We give here a quick reminder of the fundamental definitions and results of descriptor systems, such as regularity, admissibility, equivalent realizations, system decomposition, temporal response, controllability, observability, and duality.