Methods of Algebraic Geometry in Control Theory: Part I
Scalar Linear Systems and Affine Algebraic Geometry
Authors: Falb, Peter
Free Preview Provides a clear presentation of the core ideas in the algebrageometric 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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 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 algebrageometric 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)


Scalar Linear Systems over the Complex Numbers
Pages 58

Scalar Linear Systems over a Field k
Pages 914

Factoring Polynomials
Pages 1519

Affine Algebraic Geometry: Algebraic Sets
Pages 2023

Affine Algebraic Geometry: The Hilbert Theorems
Pages 2428

Table of contents (23 chapters)
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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

 Peter Falb
 Series Title
 Modern Birkhäuser Classics
 Copyright
 2018
 Publisher
 Birkhäuser Basel
 Copyright Holder
 Springer Nature Switzerland AG
 eBook ISBN
 9783319980263
 DOI
 10.1007/9783319980263
 Softcover ISBN
 9783319980256
 Series ISSN
 21971803
 Edition Number
 1
 Number of Pages
 IX, 202
 Number of Illustrations
 3 b/w illustrations
 Topics