Algebraic and Differential Methods for Nonlinear Control Theory (eBook)

Elements of Commutative Algebra and Algebraic Geometry

Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García (Autoren)

eBook Download: PDF

2019
196 Seiten
Springer International Publishing (Verlag)
978-3-030-12025-2 (ISBN)

Infos

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.

Inhalt

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.

Produkt-Details

• Erscheint lt. Verlag: 30.1.2019
• Reihe/Serie: Mathematical and Analytical Techniques with Applications to Engineering
• Reihe/Serie: Mathematical and Analytical Techniques with Applications to Engineering
• Zusatzinfo: XIV, 196 p. 13 illus., 11 illus. in color.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik
• Schlagworte: Algebraic structures for engineering mathematics • Differential Algebra for Nonlinear Control Theory • Fault Detection and Diagnosis in Nonlinear Systems • Synchronization of Coupled Fractional Order Systems • Theory of nonlinear control
• ISBN-10: 3-030-12025-2 / 3030120252
• ISBN-13: 978-3-030-12025-2 / 9783030120252