國立高雄大學圖資館 |

Language: English

Back

Methods of algebraic geometry in con...

Falb, Peter.

Methods of algebraic geometry in control theoryPart I,Scalar linear systems and affine algebraic geometry /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Methods of algebraic geometry in control theoryby Peter Falb.
remainder title:	Scalar linear systems and affine algebraic geometry
Author:	Falb, Peter.
Published:	Cham :Springer International Publishing :2018.
Description:	ix, 202 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Control theoryMathematics.
Online resource:	https://doi.org/10.1007/978-3-319-98026-3
ISBN:	9783319980263$q(electronic bk.)

Methods of algebraic geometry in control theoryPart I,Scalar linear systems and affine algebraic geometry /
Falb, Peter.

Methods of algebraic geometry in control theoryPart I,Scalar linear systems and affine algebraic geometry /[electronic resource] :Scalar linear systems and affine algebraic geometryby Peter Falb. - Cham :Springer International Publishing :2018. - ix, 202 p. :ill., digital ;24 cm. - Modern birkhauser classics,2197-1803. - Modern birkhauser classics..

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.

"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.

ISBN: 9783319980263$q(electronic bk.)

Standard No.: 10.1007/978-3-319-98026-3doiSubjects--Topical Terms:

569148
Control theory
--Mathematics.

LC Class. No.: QA402.3 / .F353 2018

Dewey Class. No.: 629.8312

Methods of algebraic geometry in control theoryPart I,Scalar linear systems and affine algebraic geometry /
LDR:03775nmm a2200349 a 4500 001 543983
003 DE-He213
005 20190304111419.0
006 m d
007 cr nn 008maaau
008 190430s2018 gw s 0 eng d
020 $a 9783319980263$q(electronic bk.)
020 $a 9783319980256$q(paper)
024 7 $a 10.1007/978-3-319-98026-3 $2 doi
035 $a 978-3-319-98026-3
040 $a GP $c GP
041 0 $a eng
050 4 $a QA402.3 $b .F353 2018
072 7 $a PBMW $2 bicssc
072 7 $a MAT012010 $2 bisacsh
072 7 $a PBMW $2 thema
082 0 4 $a 629.8312 $2 23
090 $a QA402.3 $b .F177 2018
100 1 $a Falb, Peter. $3 822428
245 1 0 $a Methods of algebraic geometry in control theory $h [electronic resource] : $n Part I, $p Scalar linear systems and affine algebraic geometry / $c by Peter Falb.
246 3 0 $a Scalar linear systems and affine algebraic geometry
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2018.
300 $a ix, 202 p. : $b ill., digital ; $c 24 cm.
490 1 $a Modern birkhauser classics, $x 2197-1803
505 0 $a 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.
520 $a "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.
650 0 $a Control theory $x Mathematics. $3 569148
650 0 $a Geometry, Algebraic. $3 190843
650 1 4 $a Algebraic Geometry. $3 274807
650 2 4 $a Systems Theory, Control. $3 274654
650 2 4 $a Control. $3 349080
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Modern birkhauser classics. $3 591811
856 4 0 $u https://doi.org/10.1007/978-3-319-98026-3
950 $a Mathematics and Statistics (Springer-11649)