Overview
- Self-contained and concise primer
- Geared towards applications in nonlinear control theory
- Emphasizes tools from ?commutative algebra and algebraic geometry
Part of the book series: Mathematical and Analytical Techniques with Applications to Engineering (MATE)
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Table of contents (10 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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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Authors and Affiliations
Bibliographic Information
Book Title: Algebraic and Differential Methods for Nonlinear Control Theory
Book Subtitle: Elements of Commutative Algebra and Algebraic Geometry
Authors: Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García
Series Title: Mathematical and Analytical Techniques with Applications to Engineering
DOI: https://doi.org/10.1007/978-3-030-12025-2
Publisher: Springer Cham
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Hardcover ISBN: 978-3-030-12024-5Published: 04 March 2019
Softcover ISBN: 978-3-030-12027-6Published: 28 October 2020
eBook ISBN: 978-3-030-12025-2Published: 30 January 2019
Series ISSN: 1559-7458
Series E-ISSN: 1559-7466
Edition Number: 1
Number of Pages: XIV, 196
Number of Illustrations: 2 b/w illustrations, 11 illustrations in colour
Topics: Engineering Mathematics, Applications of Nonlinear Dynamics and Chaos Theory, Control and Systems Theory, Systems Theory, Control