Alain Bensoussan & Giuseppe Da Prato 
Representation and Control of Infinite Dimensional Systems 

A new edition in a single volume Over the past decade, more and more sophisticaced mathematical tools and approaches have been incorporated in the ?eld of Control of in?nite dim- sional systems. This was motivated by a whole range of challenging appli- tions arising from new phenomenologicalstudies, technologicaldevelopments, and more stringent design requirements. At the same time, researchers and advanced engineers have been steadily using an impressive amount of very sophisticated mathematics in their analysis, synthesis, and design of systems. Whatwasregardedastooabstract, specialized, ortheoreticalin1990hasnow become a standard part of the toolkit. The decision to produce a second edition of the original 1992–1993 t- volume edition is further motivated by several other factors. Over the years the book has been recognizedas a key referencein the ?eld, and a revised and corrected edition was desirable. Even if some good books on the control of in?nite dimensional linear systems have appeared since then, we felt that the original material has not aged too much and that the breadth of its presen- tion is still attractiveand very competitive. The result is a completely revised and corrected second edition in a single convenient volume with integrated bibliography and index.

Table of Content

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.