Introduction

Abstract

The first part of this chapter constitutes a short introduction to systems theory. The basic notions of input, output and state variables are presented in abstract terms, as well as the notion of input-output operator. We discuss the main properties involved in the investigation of a system, and illustrate how distinct systems can be combined to give rise to a new system. In this framework, we also introduce the main concern of this book: how to exploit the input channel in order to control the evolution of a system. The exposition becomes more concrete in the remaining part of the chapter, where we explain how a system can be represented by certain mathematical models: impulse response, state space equations. The role of initial conditions is emphasized, in a deterministic philosophy, in connection with the notion of state variable.