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Algebraic and differential methods for nonlinear control theory : elements of commutative algebra and algebraic geometry
- 作者： Martinez-Guerra, Rafael, author.
- 其他作者：
- 其他題名：
- Mathematical and analytical techniques with applications to engineering.
- 出版： Cham : Springer International Publishing :Imprint: Springer
- 叢書名： Mathematical and analytical techniques with applications to engineering,
- 主題： Nonlinear control theory. , Geometry, Algebraic. , Commutative algebra. , Engineering Mathematics. , Applications of Nonlinear Dynamics and Chaos Theory. , Control and Systems Theory. , Systems Theory, Control.
- ISBN： 9783030120252 (electronic bk.) 、 9783030120245 (hardback) 、 9783030120276 (paperback)
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FIND@SFXID:
CGU
- 資料類型: 電子書
- 內容註: 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.
- 摘要註: 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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讀者標籤：
- 系統號： 005449290 | 機讀編目格式
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