# Methods of Algebraic Geometry in Control Theory: Part I

## Scalar Linear Systems and Affine Algebraic Geometry

• Peter Falb

Part of the Modern Birkhäuser Classics book series (MBC)

1. Front Matter
Pages i-xiii
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Pages 5-8
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25. Back Matter
Pages 168-202

### Introduction

"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.

### Keywords

affine algebraic geometry scalar linear systems tensor products fibers of morphisms controllability

#### Authors and affiliations

• Peter Falb
• 1
1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-319-98026-3
• Copyright Information Springer Nature Switzerland AG 2018
• Publisher Name Birkhäuser, Cham
• eBook Packages Mathematics and Statistics
• Print ISBN 978-3-319-98025-6
• Online ISBN 978-3-319-98026-3
• Series Print ISSN 2197-1803
• Series Online ISSN 2197-1811
• Buy this book on publisher's site