Introduction

Abstract

The primary concern of this book¹ is the control of linear infinite dimensional systems, that is, systems whose state space is infinite dimensional and its evolution is typically described by a linear partial differential equation, linear functional differential equation or linear integral equation.

The numbering of equations, theorems, propositions, lemmas, corollaries, definitions, examples, notations, and remarks is by chapter. When a reference to another chapter within a part is necessary, it is always followed by the words in Chapter and the number of the chapter: for instance “in equation (2.1) of Chapter 3”. When a reference to another chapter in a different part is necessary, it is always followed by the words of Chapter, the number of the chapter, of Part, and the number of the part: for instance “equation (2.1) in Chapter 1 of Part IV”. The text of theorems, propositions, lemmas, and corollaries is slanted; the text of definitions, examples, notations, and remarks is normal shape ended by a square □. The bibliography is by author in alphabetical order. For each author or group of coauthors, there is a numbering in square brackets starting with one. A reference to an item by a single author is of the form J. L. LIONS [4], and a reference to an item with several coauthors R. BELLMAN and K. L. COOKE [1].