Title | Algebraic and Differential Methods for Nonlinear Control Theory [electronic resource] : Elements of Commutative Algebra and Algebraic Geometry / by Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García |
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Imprint | Cham : Springer International Publishing : Imprint: Springer, 2019 |

Edition | 1st ed. 2019 |

Connect to | https://doi.org/10.1007/978-3-030-12025-2 |

Descript | XIV, 196 p. 13 illus., 11 illus. in color. online resource |

SUMMARY

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

CONTENT

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

Engineering mathematics
Systems theory
Engineering Mathematics. http://scigraph.springernature.com/things/product-market-codes/T11030
Applications of Nonlinear Dynamics and Chaos Theory. http://scigraph.springernature.com/things/product-market-codes/P33020
Control and Systems Theory. http://scigraph.springernature.com/things/product-market-codes/T19010
Systems Theory Control. http://scigraph.springernature.com/things/product-market-codes/M13070