State Space Representation

Abstract

In the previous chapter we introduced models with an input and an output. These models were described by an ordinary or partial differential equation. However, there are other possibilities to model systems with inputs and outputs. In this chapter we introduce the state space representation on a finite-dimensional state space. Later we will encounter these representations on an infinite-dimensional state space. State space representations enable us to study systems with inputs and outputs in a uniform framework. In this chapter, we show that every model described by an ordinary differential equation possesses a state space representation on a finite-dimensional state space, and that it is just a different way of writing down the system. However, this different representation turns out to be very important as we will see in the following chapters. In particular, it enables us to develop general control strategies.