MATHEMATICAL CONTROL THEORY
An Introduction
J. Zabczyk, Institute of Mathematics, Polish Academy of Sciences, Warsaw

"...the exposition is excellent...a joy to read.  The book is an excellent
one for introducing a mathematician to control theory."
                        - Bulletin of the American Mathematical Society

"The book is very well written from a mathematical point of view of control
theory.  The author deserves much credit for bringing out such a book which
is a useful and welcome addition to books on mathematics of control
theory."
                        - Control Theory and Advance Technology

Mathematical control theory is a separate branch of mathematics,which, over
a span of 150 years, has developed an extensive literature covering its
various concepts, constructions and applications. In particular, until now
a self-contained treatment of the following areas has been unavailable: the
basic theory of finite dimensional linear systems, of nonlinear systems,
optimal control and infinite dimensional linear systems. Mathematical
Control Theory: An Introduction presents, in a mathematically precise
manner, a unified introduction to deterministic control theory.

The author includes the stabilization of nonlinear systems using
topological methods, realization theory for nonlinear systems, impulsive
control and positive systems, the control of rigid bodies, the
stabilization of infinite dimensional systems and the solution of minimum
energy problems.

The book will be ideal for a beginning graduate course in mathematical
control theory or for self study by professionals needing a complete
picture of the mathematical theory that underlies the applications of
control theory.

Contents: Preface * Introduction * Part I. Elements of classical control
theory * Controllability and observability * Stability and stabilizability
* Realization theory * Systems with constraints * Part II. Nonlinear
control systems * Controllability and observability of nonlinear systems *
Stability and stabilizability * Realization theory * Part III. Optimal
control * Dynamic programming * Dynamic programming for impulse control *
The maximum principle * The existence of optimal strategies * Part IV.
Infinite dimensional linear systems * Linear control systems *
Controllability * Stability and stabilizability * Linear regulators in
Hilbert spaces * Appendix * References * Notations * Index

1993   260 pp.   Hardcover   $69.50   ISBN 0-8176-3645-5
Systems & Control: Foundations & Applications