Algebraic and differential methods for nonlinear control theory : elements of commutative algebra and algebraic geometry
著者
書誌事項
Algebraic and differential methods for nonlinear control theory : elements of commutative algebra and algebraic geometry
（Mathematical and analytical techniques with applications to engineering / Alan Jeffrey, consulting editor）
Springer, c2019
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
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.
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