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© 2008

Mathematical Control Theory

An Introduction

Textbook

Part of the Modern Birkhäuser Classics book series

Table of contents

  1. Front Matter
    Pages i-x
  2. Introduction

    1. Jerzy Zabczyk
      Pages 1-9
  3. Elements of classical control theory

    1. Jerzy Zabczyk
      Pages 10-27
    2. Jerzy Zabczyk
      Pages 28-49
    3. Jerzy Zabczyk
      Pages 50-61
    4. Jerzy Zabczyk
      Pages 62-72
  4. Nonlinear control systems

    1. Jerzy Zabczyk
      Pages 92-120
    2. Jerzy Zabczyk
      Pages 121-126
  5. Optimal control

    1. Jerzy Zabczyk
      Pages 127-141
    2. Jerzy Zabczyk
      Pages 142-151
    3. Jerzy Zabczyk
      Pages 152-169
    4. Jerzy Zabczyk
      Pages 170-175
  6. Infinite dimensional linear systems

    1. Jerzy Zabczyk
      Pages 176-205
    2. Jerzy Zabczyk
      Pages 206-220
    3. Jerzy Zabczyk
      Pages 221-231
    4. Jerzy Zabczyk
      Pages 232-243
  7. Back Matter
    Pages 244-260

About this book

Introduction

Mathematical Control Theory: An Introduction presents, in a mathematically precise manner, a unified introduction to deterministic control theory. With the exception of a few more advanced concepts required for the final part of the book, the presentation requires only a knowledge of basic facts from linear algebra, differential equations, and calculus.

In addition to classical concepts and ideas, the author covers 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.

 

"This book is designed as a graduate text on the mathematical theory of deterministic control. It covers a remarkable number of topics...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."   Bulletin of the AMS

"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

"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

Keywords

control control system control theory dynamic programming infinite dimensional linear systems linear systems mathematical control theory nonlinear control nonlinear system observability optimal control programming stability stabilization sys

Authors and affiliations

  1. 1.Institute of MathematicsPolish Academy of SciencesWarsawPoland

Bibliographic information

Reviews

"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 Birkhäuser in 1992, then reprinted with corrections in 1995. It has now been reprinted in the Modern Birkhäuser 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)