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Algebraic and differential methods f...

Martinez-Fuentes, Oscar.

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

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Algebraic and differential methods for nonlinear control theoryby Rafael Martinez-Guerra, Oscar Martinez-Fuentes, Juan Javier Montesinos-Garcia.
其他題名:	elements of commutative algebra and algebraic geometry /
作者:	Martinez-Guerra, Rafael.
其他作者:	Martinez-Fuentes, Oscar.
出版者:	Cham :Springer International Publishing :2019.
面頁冊數:	xiv, 196 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Nonlinear control theory.
電子資源:	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 /
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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.
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