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Computational Aspects of Linear Control

  • Book
  • © 2002

Overview

Editors:
  1. Claude Brezinski

    1. Université des Sciences et Technologies de Lille, France

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Part of the book series: Numerical Methods and Algorithms (NUAL, volume 1)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-ix
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  2. Introduction

    • Claude Brezinski
    Pages 1-2

  3. Control of Linear Systems

    • Claude Brezinski
    Pages 3-72

  4. Formal Orthogonal Polynomials

    • Claude Brezinski
    Pages 73-85

  5. Padé Approximations

    • Claude Brezinski
    Pages 87-134

  6. Transform Inversion

    • Claude Brezinski
    Pages 135-143

  7. Linear Algebra Issues

    • Claude Brezinski
    Pages 145-159

  8. Lanczos Tridiagonalization Process

    • Claude Brezinski
    Pages 161-169

  9. Systems of Linear Algebraic Equations

    • Claude Brezinski
    Pages 171-223

  10. Regularization of Ill-Conditioned Systems

    • Claude Brezinski
    Pages 225-247

  11. Sylvester and Riccati Equations

    • Claude Brezinski
    Pages 249-253

  12. Topics on Nonlinear Differential Equations

    • Claude Brezinski
    Pages 255-275

  13. Appendix: The Mathematics of Model Reduction

    • Claude Brezinski
    Pages 277-287

  14. Back Matter

    Pages 289-295
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Keywords

About this book

Many devices (we say dynamical systems or simply systems) behave like black boxes: they receive an input, this input is transformed following some laws (usually a differential equation) and an output is observed. The problem is to regulate the input in order to control the output, that is for obtaining a desired output. Such a mechanism, where the input is modified according to the output measured, is called feedback. The study and design of such automatic processes is called control theory. As we will see, the term system embraces any device and control theory has a wide variety of applications in the real world. Control theory is an interdisci­ plinary domain at the junction of differential and difference equations, system theory and statistics. Moreover, the solution of a control problem involves many topics of numerical analysis and leads to many interesting computational problems: linear algebra (QR, SVD, projections, Schur complement, structured matrices, localization of eigenvalues, computation of the rank, Jordan normal form, Sylvester and other equations, systems of linear equations, regulariza­ tion, etc), root localization for polynomials, inversion of the Laplace transform, computation of the matrix exponential, approximation theory (orthogonal poly­ nomials, Pad6 approximation, continued fractions and linear fractional transfor­ mations), optimization, least squares, dynamic programming, etc. So, control theory is also a. good excuse for presenting various (sometimes unrelated) issues of numerical analysis and the procedures for their solution. This book is not a book on control.

Reviews

From the reviews:
"[...]there are very few books, if any, which combine control theory and relevant numerical techniques. The present book under review, Computational Aspects of Linear Control, by Claude Brezinski, is exactly such a book."
(Ezra Zeheb, Technion-Israel Institute of Technology)

Editors and Affiliations

  • Université des Sciences et Technologies de Lille, France

    Claude Brezinski

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