Introduction

Abstract

Most real systems evolve in continuous time and thus are described by differential equations. However, in practice any data collected from a given system or any update of their input signal is performed at specific sampling instants. Thus, sampled data models are required in control, estimation, and system identification. In this chapter we discuss the elements present in the sampling process, namely, the continuous-time system, the hold device used to generate the continuous-time input from a sequence of samples, the antialiasing filter, and the sampler used to obtain a discrete-time sequence from the continuous-time output. We also present the main questions that motivate our book: what are the characteristics of the sampled models that can be associated with the underlying continuous-time system and what are artifacts due the sampling process? Can we recover the continuous-time system description from the sampled model by increasing the sampling frequency? What are the most important issues to be taken into account when using a discrete-time model to represent a continuous-time system? And how can sampled-data models for linear systems be extended for nonlinear systems?