Modern Birkhäuser Classics

Methods of Algebraic Geometry in Control Theory: Part I

Scalar Linear Systems and Affine Algebraic Geometry

Authors: Falb, Peter

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  • Provides ​a clear presentation of the core ideas in the algebra-geometric treatment of scalar linear system theory with an applied flavor
  • Makes the basic ideas of algebraic geometry accessible to engineers and applied scientists
  • Introduces the four representations of a scalar linear system and establishes the major results of a similar theory for multivariable systems
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eBook $39.99
price for USA in USD (gross)
  • ISBN 978-3-319-98026-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA in USD
  • ISBN 978-3-319-98025-6
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  • Usually dispatched within 3 to 5 business days.
About this Textbook

"An introduction to the ideas of algebraic geometry in the motivated context of system theory." Thus the author describes his textbook that has been specifically written to serve the needs of students of systems and control. Without sacrificing mathematical care, the author makes the basic ideas of algebraic geometry accessible to engineers and applied scientists. The emphasis is on constructive methods and clarity rather than abstraction. 
The student will find here a clear presentation with an applied flavor, of the core ideas in the algebra-geometric treatment of scalar linear system theory. The author introduces the four representations of a scalar linear system and establishes the major results of a similar theory for multivariable systems appearing in a succeeding volume (Part II: Multivariable Linear Systems and Projective Algebraic Geometry). 
Prerequisites are the basics of linear algebra, some simple notions from topology and the elementary properties of groups, rings, and fields, and a basic course in linear systems. Exercises are an integral part of the treatment and are used where relevant in the main body of the text. The present, softcover reprint is designed to make this classic textbook available to a wider audience.
"This book is a concise development of affine algebraic geometry together with very explicit links to the applications...[and] should address a wide community of readers, among pure and applied mathematicians." —Monatshefte für Mathematik

About the authors

Peter Falb is a Professor Emeritus of Applied Mathematics at Brown University.

Table of contents (23 chapters)

Table of contents (23 chapters)

Buy this book

eBook $39.99
price for USA in USD (gross)
  • ISBN 978-3-319-98026-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA in USD
  • ISBN 978-3-319-98025-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Methods of Algebraic Geometry in Control Theory: Part I
Book Subtitle
Scalar Linear Systems and Affine Algebraic Geometry
Authors
Series Title
Modern Birkhäuser Classics
Copyright
2018
Publisher
Birkhäuser Basel
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-319-98026-3
DOI
10.1007/978-3-319-98026-3
Softcover ISBN
978-3-319-98025-6
Series ISSN
2197-1803
Edition Number
1
Number of Pages
IX, 202
Number of Illustrations
3 b/w illustrations
Topics