Semigroup Theory

Abstract

The examples of infinite-dimensional systems we introduced in Chapter 1 were either partial or delay differential equations. The theme of this book is to describe them through an abstract formulation of the type

$$\begin{array}{*{20}{c}}{\dot z\left( t \right) = Az\left( t \right) + Bu\left( t \right),{\text{ t}} \geqslant {\text{0,}}}&{z\left( 0 \right) = {z_0},}\end{array}$$

(2.1)

on a separable complex Hilbert space Z to enable us to present a unified treatment of these and finite-dimensional systems. Let us first consider a simple example.