"This book is a most welcome addition to the literature of this field, where it serves the need for a modern treatment on topics that only very recently have found a satisfactory solution.... Many readers will appreciate the concise exposition."

"The quadratic cost optimal control problem for systems described by linear ordinary differential equations occupies a central role in the study of control systems both from a theoretical and design point of view. The study of this problem over an infinite time horizon shows the beautiful interplay between optimality and the qualitative properties of systems such as controllability, observability, and stabilizability. This theory is far more difficult for infinite-dimensional systems such as those with time delays and distributed parameter systems. This unified revised edition of a two-volume set is a self-contained account of quadratic cost optimal control for a large class of infinite-dimensional systems.Material new to the second edition includes a section on finite-dimensional system, which provides a reorganized introduction to the control of linear systems, and a chapter on linear quadratic differential games. New results using the invariant embedding approach are included to provide further insight into the associated min-sup and max-inf problems. A unique chapter on semigroup theory 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 with these applications, which arise from new phenomenal studies, new technological developments, and more stringent design requirements. It will be useful for mathematicians, researchers, graduate students, and engineers interested in the field and the underlying tenets of control.TOC:Preface to the Second Edition.- Preface to Volume I of the First Edition.- Preface to Volume II of the First Edition.- Introduction.- Part I. Finite Dimensional Linear Control of Dynamical Systems.- Control of Linear Finite Dimensional Differential Systems.- Linear Quadratic Two-Person Zero-Sum Differential Games.- Part II. Representation of Infinite Dimensional Linear Control Dynamical Systems.- Semi-groups of Operators and Interpolation.- Variational Theory of Parabolic Systems.- Semi-group Methods for Systems with Unbounded Control and Observation Operators.- Differential Systems with Delays.- Part III. Qualitative Properties of Linear Control Dynamical Systems.- Controllability and Observability for a Class of Infinite Dimensional Systems.- Part IV. Quadratic Optimal Control: Finite Time Horizon.- Systems with Bounded Control Operators: Control Inside the Domain.- Systems with Unbounded Control Operators: Parabolic Equations with Control on the Boundary.- Systems with Unbounded Control Operators: Hyperbolic Equations with Control on the Boundary.- Part V. Quadratic Optimal Control: Infinite Time Horizon.- Systems with Bounded Control Operators: Control Inside the Domain.- Systems with Unbounded Control Operators: Parabolic Equations with Control on the Boundary.- Systems with Unbounded Control Operators: Hyperbolic Equations with Control on the Boundary.- Appendix A. An Isomorphism Result.- References.- Index"

Finite Dimensional Linear Control Dynamical Systems.- Control of Linear Differential Systems.- Linear Quadratic Two-Person Zero-Sum Differential Games.- Representation of Infinite Dimensional Linear Control Dynamical Systems.- Semigroups of Operators and Interpolation.- Variational Theory of Parabolic Systems.- Semigroup Methods for Systems With Unbounded Control and Observation Operators.- State Space Theory of Differential Systems With Delays.- Qualitative Properties of Infinite Dimensional Linear Control Dynamical Systems.- Controllability and Observability for a Class of Infinite Dimensional Systems.- Quadratic Optimal Control: Finite Time Horizon.- Bounded Control Operators: Control Inside the Domain.- Unbounded Control Operators: Parabolic Equations With Control on the Boundary.- Unbounded Control Operators: Hyperbolic Equations With Control on the Boundary.- Quadratic Optimal Control: Infinite Time Horizon.- Bounded Control Operators: Control Inside the Domain.- Unbounded Control Operators: Parabolic Equations With Control on the Boundary.- Unbounded Control Operators: Hyperbolic Equations With Control on the Boundary.