Mathematical Control Theory

• Elements of classical control theory.- Controllability and observability.- Stability and stabilizability.- Realization theory.- Systems with constraints.- Nonlinear control systems.- Controllability and observability of nonlinear systems.- Stability and stabilizability.- Realization theory.- Optimal control.- Dynamic programming.- Dynamic programming for impulse control.- The maximum principle.- The existence of optimal strategies.- Infinite dimensional linear systems.- Linear control systems.- Controllability.- Stability and stabilizability.- Linear regulators in Hilbert spaces.

"Many textbooks and monographs in the existing literature focus on specific control problems or systems, such as linear or nonlinear, finite-dimensional or infinite-dimensional, continuous-time, discrete-time, or discrete-event dynamical systems...However, Mathematical Control Theory is of a different style, which makes it unique in the book market. This ambitious book sets its target at fundamental problems, including structural properties such as controllability and observability, for a variety of mathematical models. The 260-page book covers a remarkably wide range of materials...The contents of this well-organized book mainly include the analysis of control properties and optimization. I enjoyed reading the concise mathematical description with [its] clean logical structure. I also learned several new things or reviewed some materials from new angles... I recommend the book to readers who are interested in the rigorous mathematical buildup of control systems and problems. Indeed, for mathematicians who look for the basic ideas or a general picture about the main branches of control theory, I believe this book can provide an excellent bridge to this area. Finally, for students who are ready for a more rigorous approach after grasping suitable mathematical preliminaries and control engineering background, this book can be helpful owing to its theoretical beauty and clarity." -IEEE Control Systems Magazine (Review of the Reprinted Softcover Edition) "This introduction to Mathematical Control Theory was first published by Birkhauser in 1992, then reprinted with corrections in 1995. It has now been reprinted in the Modern Birkhauser Classics series...This is a worthy reprint of a worthy book." -MAA Reviews (Review of the Reprinted Softcover Edition) "This book is designed as a graduate text on the mathematical theory of deterministic control. It covers a remarkable number of topics... The book includes material on the realization of both linear and nonlinear systems, impulsive control, and positive linear systems-subjects not usually covered in an 'introductory' book... To get so much material in such a short space, the pace of the presentation is brisk. However, the exposition is excellent, and the book is a joy to read. A novel one-semester course covering both linear and nonlinear systems could be given... The book is an excellent one for introducing a mathematician to control theory. The book presents a large amount of material very well, and its use is highly recommended." -Bulletin of the AMS (Review of the Original Hardcover Edition) "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 the mathematics of control theory." -Control Theory and Advance Technology (Review of the Original Hardcover Edition) "At last! We did need an introductory textbook on control which can be read, understood, and enjoyed by anyone." -Gian-Carlo Rota, The Bulletin of Mathematics Books (Review of the Original Hardcover Edition)