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© 2020

Algebraic and Symbolic Computation Methods in Dynamical Systems

  • Alban Quadrat
  • Eva Zerz
Book

Part of the Advances in Delays and Dynamics book series (ADVSDD, volume 9)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Effective Algebraic Methods for Linear Functional Systems

    1. Front Matter
      Pages 1-1
    2. T. Cluzeau, C. Koutschan, A. Quadrat, M. Tõnso
      Pages 3-52
    3. Thomas Cluzeau, Alban Quadrat
      Pages 53-86
  3. Symbolic Methods for Nonlinear Dynamical Systems and for Applications to Observation and Estimation Problems

    1. Front Matter
      Pages 115-115
    2. Markus Lange-Hegermann, Daniel Robertz
      Pages 117-146
    3. François Boulier, François Lemaire, Markus Rosenkranz, Rosane Ushirobira, Nathalie Verdière
      Pages 161-182
    4. Rosane Ushirobira, Anja Korporal, Wilfrid Perruquetti
      Pages 183-200
  4. Algebraic Geometry Methods for Systems and Control Theory

    1. Front Matter
      Pages 201-201
    2. Islam Boussaada, Silviu-Iulian Niculescu
      Pages 239-258
    3. Christian Schilli, Eva Zerz, Viktor Levandovskyy
      Pages 259-293
    4. Ricardo Pereira, Paula Rocha
      Pages 295-306
  5. Back Matter
    Pages 307-311

About this book

Introduction

This book aims at reviewing recent progress in the direction of algebraic and symbolic computation methods for functional systems, e.g. ODE systems, differential time-delay equations, difference equations and integro-differential equations. In the nineties, modern algebraic theories were introduced in mathematical systems theory and in control theory. Combined with real algebraic geometry, which was previously introduced in control theory, the past years have seen a flourishing development of algebraic methods in control theory. One of the strengths of algebraic methods lies in their close connections to computations. The use of the above-mentioned algebraic theories in control theory has been an important source of motivation to develop effective versions of these theories (when possible). With the development of computer algebra and computer algebra systems, symbolic methods for control theory have been developed over the past years. The goal of this book is to propose a partial state of the art in this direction. To make recent results more easily accessible to a large audience, the chapters include materials which survey the main mathematical methods and results and which are illustrated with explicit examples.

Keywords

Algebraic Theories Control Theory Computer Algebra System Symbolic Computation Method Algebraic Computation Methods

Editors and affiliations

  • Alban Quadrat
    • 1
  • Eva Zerz
    • 2
  1. 1.Inria Paris, Institut de Mathématiques de Jussieu-Paris Rive GaucheSorbonne UniversityParisFrance
  2. 2.Lehrstuhl D fuer MathematikRWTH Aachen UniversityAachenGermany

Bibliographic information

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