國立高雄大學圖資館 |

Language: English

Back

Algebraic and differential methods f...

Martinez-Fuentes, Oscar.

Algebraic and differential methods for nonlinear control theoryelements of commutative algebra and algebraic geometry /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Algebraic and differential methods for nonlinear control theoryby Rafael Martinez-Guerra, Oscar Martinez-Fuentes, Juan Javier Montesinos-Garcia.
Reminder of title:	elements of commutative algebra and algebraic geometry /
Author:	Martinez-Guerra, Rafael.
other author:	Martinez-Fuentes, Oscar.
Published:	Cham :Springer International Publishing :2019.
Description:	xiv, 196 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Nonlinear control theory.
Online resource:	https://doi.org/10.1007/978-3-030-12025-2
ISBN:	9783030120252$q(electronic bk.)

Algebraic and differential methods for nonlinear control theoryelements of commutative algebra and algebraic geometry /
Martinez-Guerra, Rafael.

Algebraic and differential methods for nonlinear control theoryelements of commutative algebra and algebraic geometry /[electronic resource] :by Rafael Martinez-Guerra, Oscar Martinez-Fuentes, Juan Javier Montesinos-Garcia. - Cham :Springer International Publishing :2019. - xiv, 196 p. :ill., digital ;24 cm. - Mathematical and analytical techniques with applications to engineering,1559-7458. - Mathematical and analytical techniques with applications to engineering..

Mathematical Background -- Group Theory -- Rings -- Matrices and linear equations systems -- Permutations and Determinants -- Vector and Euclidean Spaces -- Linear Transformations -- Matrix Diagonalization and Jordan Canonical Form -- Differential Equations -- Differential Algebra for Nonlinear Control Theory -- Appendix -- Index.

This book is a short primer in engineering mathematics with a view on applications in nonlinear control theory. In particular, it introduces some elementary concepts of commutative algebra and algebraic geometry which offer a set of tools quite different from the traditional approaches to the subject matter. This text begins with the study of elementary set and map theory. Chapters 2 and 3 on group theory and rings, respectively, are included because of their important relation to linear algebra, the group of invertible linear maps (or matrices) and the ring of linear maps of a vector space. Homomorphisms and Ideals are dealt with as well at this stage. Chapter 4 is devoted to the theory of matrices and systems of linear equations. Chapter 5 gives some information on permutations, determinants and the inverse of a matrix. Chapter 6 tackles vector spaces over a field, Chapter 7 treats linear maps resp. linear transformations, and in addition the application in linear control theory of some abstract theorems such as the concept of a kernel, the image and dimension of vector spaces are illustrated. Chapter 8 considers the diagonalization of a matrix and their canonical forms. Chapter 9 provides a brief introduction to elementary methods for solving differential equations and, finally, in Chapter 10, nonlinear control theory is introduced from the point of view of differential algebra.

ISBN: 9783030120252$q(electronic bk.)

Standard No.: 10.1007/978-3-030-12025-2doiSubjects--Topical Terms:

182079
Nonlinear control theory.

LC Class. No.: QA402.35 / .M378 2019

Dewey Class. No.: 629.836

Algebraic and differential methods for nonlinear control theoryelements of commutative algebra and algebraic geometry /
LDR:02972nmm a2200349 a 4500 001 552840
003 DE-He213
005 20190806164901.0
006 m d
007 cr nn 008maaau
008 191107s2019 gw s 0 eng d
020 $a 9783030120252$q(electronic bk.)
020 $a 9783030120245$q(hardback)
020 $a 9783030120276$q(paperback)
024 7 $a 10.1007/978-3-030-12025-2 $2 doi
035 $a 978-3-030-12025-2
040 $a GP $c GP
041 0 $a eng
050 4 $a QA402.35 $b .M378 2019
072 7 $a TBJ $2 bicssc
072 7 $a TEC009000 $2 bisacsh
072 7 $a TBJ $2 thema
082 0 4 $a 629.836 $2 23
090 $a QA402.35 $b .M385 2019
100 1 $a Martinez-Guerra, Rafael. $3 677674
245 1 0 $a Algebraic and differential methods for nonlinear control theory $h [electronic resource] : $b elements of commutative algebra and algebraic geometry / $c by Rafael Martinez-Guerra, Oscar Martinez-Fuentes, Juan Javier Montesinos-Garcia.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2019.
300 $a xiv, 196 p. : $b ill., digital ; $c 24 cm.
490 1 $a Mathematical and analytical techniques with applications to engineering, $x 1559-7458
505 0 $a Mathematical Background -- Group Theory -- Rings -- Matrices and linear equations systems -- Permutations and Determinants -- Vector and Euclidean Spaces -- Linear Transformations -- Matrix Diagonalization and Jordan Canonical Form -- Differential Equations -- Differential Algebra for Nonlinear Control Theory -- Appendix -- Index.
520 $a This book is a short primer in engineering mathematics with a view on applications in nonlinear control theory. In particular, it introduces some elementary concepts of commutative algebra and algebraic geometry which offer a set of tools quite different from the traditional approaches to the subject matter. This text begins with the study of elementary set and map theory. Chapters 2 and 3 on group theory and rings, respectively, are included because of their important relation to linear algebra, the group of invertible linear maps (or matrices) and the ring of linear maps of a vector space. Homomorphisms and Ideals are dealt with as well at this stage. Chapter 4 is devoted to the theory of matrices and systems of linear equations. Chapter 5 gives some information on permutations, determinants and the inverse of a matrix. Chapter 6 tackles vector spaces over a field, Chapter 7 treats linear maps resp. linear transformations, and in addition the application in linear control theory of some abstract theorems such as the concept of a kernel, the image and dimension of vector spaces are illustrated. Chapter 8 considers the diagonalization of a matrix and their canonical forms. Chapter 9 provides a brief introduction to elementary methods for solving differential equations and, finally, in Chapter 10, nonlinear control theory is introduced from the point of view of differential algebra.
650 0 $a Nonlinear control theory. $3 182079
650 0 $a Geometry, Algebraic. $3 190843
650 0 $a Commutative algebra. $3 190842
650 1 4 $a Engineering Mathematics. $3 806481
650 2 4 $a Applications of Nonlinear Dynamics and Chaos Theory. $3 760027
650 2 4 $a Control and Systems Theory. $3 825946
650 2 4 $a Systems Theory, Control. $3 274654
700 1 $a Martinez-Fuentes, Oscar. $3 833748
700 1 $a Montesinos-Garcia, Juan Javier. $3 833749
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Mathematical and analytical techniques with applications to engineering. $3 727898
856 4 0 $u https://doi.org/10.1007/978-3-030-12025-2
950 $a Engineering (Springer-11647)