Algebraic and Geometric Methods in Nonlinear Control Theory

  • M. Fliess
  • M. Hazewinkel

Part of the Mathematics and Its Applications book series (MAIA, volume 29)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Controllability, Observability, Realization and other Structural Properties

    1. Front Matter
      Pages 1-1
    2. Zbigniew Bartosiewicz
      Pages 45-54
    3. P. E. Crouch, C. I. Byrnes
      Pages 55-75
    4. Arthur J. Krener
      Pages 77-87
  3. Feedback Synthesis and Linearization Techniques

  4. Optimal Control

    1. Front Matter
      Pages 323-323
    2. I. A. K. Kupka
      Pages 347-369
    3. Michel Fliess, Françoise Lamnabhi-Lagarrigue
      Pages 371-387
    4. A. J. van der Schaft
      Pages 389-407
  5. Discrete-Time Systems

    1. Front Matter
      Pages 409-409
    2. S. Monaco, D. Normand-Cyrot
      Pages 411-430
    3. Eduardo D. Sontag
      Pages 441-483
  6. Various other Theoretical Aspects

    1. Front Matter
      Pages 485-485
    2. Anthony M. Bloch, Christopher I. Byrnes
      Pages 487-498
    3. C. Hespel, G. Jacob
      Pages 511-520
  7. Applications

  8. Back Matter
    Pages 633-642

About this book


Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point"of a Pin'. van GuIik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non­ trivially) in regional and theoretical economics; algebraic geometry interacts with physics; ihe Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras ·are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.


algebra algebraic geometry coding theory homotopy lie algebra transformation

Editors and affiliations

  • M. Fliess
    • 1
  • M. Hazewinkel
    • 2
  1. 1.Laboratoire des Signaux et SystèmesCNRS — École Supérieure d’ElectricitéGif-sur-YvetteFrance
  2. 2.Centre for Mathematics and Computer ScienceAmsterdamThe Netherlands

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media B.V. 1986
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-010-8593-9
  • Online ISBN 978-94-009-4706-1
  • Buy this book on publisher's site