Softcover ISBN:  9780821849187 
Product Code:  SURV/136.S 
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eBook ISBN:  9781470413637 
Product Code:  SURV/136.S.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9780821849187 
eBook: ISBN:  9781470413637 
Product Code:  SURV/136.S.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 
Softcover ISBN:  9780821849187 
Product Code:  SURV/136.S 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470413637 
Product Code:  SURV/136.S.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9780821849187 
eBook ISBN:  9781470413637 
Product Code:  SURV/136.S.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 

Book DetailsMathematical Surveys and MonographsVolume: 136; 2007; 426 ppMSC: Primary 93; Secondary 35
This book presents methods to study the controllability and the stabilization of nonlinear control systems in finite and infinite dimensions. The emphasis is put on specific phenomena due to nonlinearities. In particular, many examples are given where nonlinearities turn out to be essential to get controllability or stabilization. Various methods are presented to study the controllability or to construct stabilizing feedback laws. The power of these methods is illustrated by numerous examples coming from such areas as celestial mechanics, fluid mechanics, and quantum mechanics.
The book is addressed to graduate students in mathematics or control theory, and to mathematicians or engineers with an interest in nonlinear control systems governed by ordinary or partial differential equations.
ReadershipGraduate students and research mathematicians interested in control theory and nonlinear partial differential equations.

Table of Contents

Chapters

1. Finitedimensional linear control systems

2. Linear partial differential equations

3. Controllability of nonlinear systems in finite dimension

4. Linearized control systems and fixedpoint methods

5. Iterated Lie brackets

6. Return method

7. Quasistatic deformations

8. Power series expansion

9. Previous methods applied to a Schrödinger equation

10. Linear control systems in finite dimension and applications to nonlinear control systems

11. Stabilization of nonlinear control systems in finite dimension

12. Feedback design tools

13. Applications to some partial differential equations


Additional Material

Reviews

This well written book by JeanMichel Coron, one of the world leading experts in the field, enables the reader to enter the difficult subject and to understand the most important methods used here. A book like this was urgently needed.
Zentralblatt MATH 
Throughout of the book, the author gives extensive historical comments and he mentions a great number of additional results.
Mathematical Reviews


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This book presents methods to study the controllability and the stabilization of nonlinear control systems in finite and infinite dimensions. The emphasis is put on specific phenomena due to nonlinearities. In particular, many examples are given where nonlinearities turn out to be essential to get controllability or stabilization. Various methods are presented to study the controllability or to construct stabilizing feedback laws. The power of these methods is illustrated by numerous examples coming from such areas as celestial mechanics, fluid mechanics, and quantum mechanics.
The book is addressed to graduate students in mathematics or control theory, and to mathematicians or engineers with an interest in nonlinear control systems governed by ordinary or partial differential equations.
Graduate students and research mathematicians interested in control theory and nonlinear partial differential equations.

Chapters

1. Finitedimensional linear control systems

2. Linear partial differential equations

3. Controllability of nonlinear systems in finite dimension

4. Linearized control systems and fixedpoint methods

5. Iterated Lie brackets

6. Return method

7. Quasistatic deformations

8. Power series expansion

9. Previous methods applied to a Schrödinger equation

10. Linear control systems in finite dimension and applications to nonlinear control systems

11. Stabilization of nonlinear control systems in finite dimension

12. Feedback design tools

13. Applications to some partial differential equations

This well written book by JeanMichel Coron, one of the world leading experts in the field, enables the reader to enter the difficult subject and to understand the most important methods used here. A book like this was urgently needed.
Zentralblatt MATH 
Throughout of the book, the author gives extensive historical comments and he mentions a great number of additional results.
Mathematical Reviews