This reorganized, revised, and expanded edition of a two-volume set is a self-contained account of quadratic cost optimal control for a large class of infinite dimensional systems. The study of this problem shows the beautiful interplay between optimality and the qualitative properties of systems such as controllability, observability, stabilizability, and detectability.

New material includes an expanded chapter on the control of linear systems and a chapter on linear quadratic two-person zero-sum differential games. A unique chapter on semigroup theory and interpolation of linear operators brings together advanced concepts and techniques that are usually treated independently. The material on delay systems and structural operators is not available elsewhere in book form.

Control of infinite dimensional systems has a wide range and growing number of challenging applications. This book is a key reference for anyone working on these applications, which arise from new phenomenological studies, new technological developments, and more stringent design requirements. It will be useful for mathematicians, graduate students, and engineers interested in the field and in the underlying conceptual ideas of systems and control.