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Algebraic and Differential Methods for Nonlinear Control Theory

Elements of Commutative Algebra and Algebraic Geometry

  • Rafael Martínez-Guerra
  • Oscar Martínez-Fuentes
  • Juan Javier Montesinos-García

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García
    Pages 1-17
  3. Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García
    Pages 19-30
  4. Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García
    Pages 31-47
  5. Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García
    Pages 49-64
  6. Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García
    Pages 65-73
  7. Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García
    Pages 75-91
  8. Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García
    Pages 93-107
  9. Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García
    Pages 109-123
  10. Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García
    Pages 125-161
  11. Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García
    Pages 163-182
  12. Back Matter
    Pages 183-196

About this book

Introduction

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.

Keywords

Fault Detection and Diagnosis in Nonlinear Systems Differential Algebra for Nonlinear Control Theory Synchronization of Coupled Fractional Order Systems Theory of nonlinear control Algebraic structures for engineering mathematics

Authors and affiliations

  • Rafael Martínez-Guerra
    • 1
  • Oscar Martínez-Fuentes
    • 2
  • Juan Javier Montesinos-García
    • 3
  1. 1.Departamento de Control AutomáticoCINVESTAV-IPNMexico CityMexico
  2. 2.Departamento de Control AutomáticoCINVESTAV-IPNMexico CityMexico
  3. 3.Departamento de Control AutomáticoCINVESTAV-IPNMexico CityMexico

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-12025-2
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-030-12024-5
  • Online ISBN 978-3-030-12025-2
  • Series Print ISSN 1559-7458
  • Series Online ISSN 1559-7466
  • Buy this book on publisher's site