Introduction

Abstract

Due to the fact that there have been many recent papers, books and PhD-theses on the H _∞-control problem, there are few members of the systems & control community who have not at least heard of this problem. The reason for all the research in this field is that a lot of interesting control problems can be formulated in a general H _∞-design framework (see e.g. Francis [34] and references therein); in particular, we mention several robustness optimization problems and the so-called mixed-sensitivity problem. In order to explain what H _∞-control is about, we shall introduce the problem in Section 1.1 below, without mentioning all the technical details, and we shall give some examples. Furthermore, we shall discuss the relevant literature on the state-space approach to this problem, both for finite-dimensional systems and distributed parameter systems (we shall often also use the term infinite-dimensional systems). In Section 1.2 we shall introduce our class of distributed parameter systems, again without going into too much detail, and some examples will be given in order to motivate the choice of this class. In Section 1.3 an outline of the rest of the book is given.