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Methods of Algebraic Geometry in Control Theory: Part I: Scalar Linear Systems and Affine Algebraic Geometry de Peter Falb

Methods of Algebraic Geometry in Control Theory: Part I: Scalar Linear Systems and Affine Algebraic Geometry: Modern Birkhäuser Classics

Autor Peter Falb
en Limba Engleză Paperback – 3 sep 2018
"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 topologyand 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
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Paperback (4) 38333 lei  6-8 săpt.
  Springer International Publishing – 3 sep 2018 38333 lei  6-8 săpt.
  Springer International Publishing – 2 oct 2018 42749 lei  6-8 săpt.
  Birkhäuser Boston – 12 iun 2012 63580 lei  6-8 săpt.
  Birkhäuser Boston – 8 oct 2012 64560 lei  6-8 săpt.
Hardback (2) 64268 lei  6-8 săpt.
  Birkhäuser Boston – iul 1990 64268 lei  6-8 săpt.
  Birkhäuser Boston – feb 2000 65199 lei  6-8 săpt.

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Specificații

ISBN-13: 9783319980256
ISBN-10: 3319980254
Pagini: 202
Ilustrații: IX, 202 p. 3 illus.
Dimensiuni: 155 x 235 x 14 mm
Greutate: 0.3 kg
Ediția:1st ed. 2018
Editura: Springer International Publishing
Colecția Birkhäuser
Seria Modern Birkhäuser Classics

Locul publicării:Cham, Switzerland

Cuprins

0. Introduction.- 1. Scalar Linear Systems over the Complex Numbers.- 2. Scalar Linear Systems over a Field k.- 3. Factoring Polynomials.- 4. Affine Algebraic Geometry: Algebraic Sets.- 5. Affine Algebraic Geometry: The Hilbert Theorems.- 6. Affine Algebraic Geometry: Irreducibility.- 7. Affine Algebraic Geometry: Regular Functions and Morphisms I.- 8. The Laurent Isomorphism Theorem.- 9. Affine Algebraic Geometry: Regular Functions and Morphisms II.- 10. The State Space: Realizations.- 11. The State Space: Controllability, Observability, Equivalence.- 12. Affine Algebraic Geometry: Products, Graphs and Projections.- 13. Group Actions, Equivalence and Invariants.- 14. The Geometric Quotient Theorem: Introduction.- 15. The Geometric Quotient Theorem: Closed Orbits.- 16. Affine Algebraic Geometry: Dimension.- 17. The Geometric Quotient Theorem: Open on Invariant Sets.- 18. Affine Algebraic Geometry: Fibers of Morphisms.- 19. The Geometric Quotient Theorem: The Ring of Invariants.- 20. Affine Algebraic Geometry: Simple Points.- 21. Feedback and the Pole Placement Theorem.- 22. Affine Algebraic Geometry: Varieties.- 23. Interlude.- Appendix A: Tensor Products.- Appendix B: Actions of Reductive Groups.- Appendix C: Symmetric Functions and Symmetric Group Actions.- Appendix D: Derivations and Separability.- Problems.- References.

Notă biografică

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

Textul de pe ultima copertă

"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 topologyand 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.


Caracteristici

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

Recenzii

"The exposition is extremely clear. In order to motivate the general theory, the author presents a number of examples of two or three input-, two-output systems in detail. I highly recommend this excellent book to all those interested in the interplay between control theory and algebraic geometry." —Publicationes Mathematicae, Debrecen
"This book is the multivariable counterpart of Methods of Algebraic Geometry in Control Theory, Part I…. In the first volume the simpler single-input–single-output time-invariant linear systems were considered and the corresponding simpler affine algebraic geometry was used as the required prerequisite. Obviously, multivariable systems are more difficult and consequently the algebraic results are deeper and less transparent, but essential in the understanding of linear control theory…. Each chapter contains illustrative examples throughout and terminates with some exercises for further study." —Mathematical Reviews