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Three Decades of Mathematical System Theory

A Collection of Surveys at the Occasion of the 50th Birthday of Jan C. Willems

  • Book
  • © 1989

Overview

Editors:
  1. Hendrik Nijmeijer
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  2. Johannes M. Schumacher
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Part of the book series: Lecture Notes in Control and Information Sciences (LNCIS, volume 135)

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Table of contents (21 chapters)

  1. Front Matter

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  2. The cascade structure in system theory

    • A. C. Antoulas
    Pages 1-18

  3. Smooth dynamical systems which realize arithmetical and logical operations

    • R. W. Brockett
    Pages 19-30

  4. Pole assignment by output feedback

    • C. I. Byrnes
    Pages 31-78

  5. Zeros, poles and modules in linear system theory

    • G. Conte, A. M. Perdon
    Pages 79-100

  6. Representations of infinite-dimensional systems

    • R. F. Curtain
    Pages 101-128

  7. Symmetric modeling in system identification

    • M. Deistler
    Pages 129-147

  8. Elements of factorization theory from a polynomial point of view

    • P. A. Fuhrmann
    Pages 148-178

  9. A state space approach to H ∞ optimal control

    • K. Glover, J. C. Doyle
    Pages 179-218

  10. Decentralized control of large scale systems

    • M. Ikeda
    Pages 219-242

  11. State space approach to the classical interpolation problem and its applications

    • H. Kimura
    Pages 243-275

  12. Generalized state-space systems and proper stable matrix fractions

    • V. Kučera
    Pages 276-301

  13. Scattering theory, unitary dilations and Gaussian processes

    • S. K. Mitter, Y. B. Avniel
    Pages 302-338

  14. On the theory of nonlinear control systems

    • H. Nijmeijer
    Pages 339-357

  15. Aggregation of linear systems in a completely deterministic framework

    • G. Picci
    Pages 358-381

  16. Linear system representations

    • J. M. Schumacher
    Pages 382-408

  17. Optimal Control

    • H. J. Sussmann
    Pages 409-425

  18. System theory and mechanics

    • A. J. van der Schaft
    Pages 426-452

  19. The impact of the singular value decomposition in system theory, signal processing, and circuit theory

    • J. Vandewalle, L. Vandenberghe, M. Moonen
    Pages 453-479

  20. Stochastic realization problems

    • J. H. van Schuppen
    Pages 480-523
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Keywords

About this book

The field of modern mathematical system theory has its origins in the work of R.E. Kalman in the late fifties. It came to a rapid development in the early sixties, and has seen a continuing and still growing stream of contributions in the years that followed. Today, it stands as a well-established discipline. The volume Three Decades of Mathematical System Theory surveys the developments in this field by presenting 21 articles covering the broad area of system and control theory. All articles have been written by well-known authors, who were invited to give their personal expert view on a particular direction of research. Together, the contributions in this volume review the wide range of mathematical methods that are being applied in modern system and control theory. The mathematical fields that are involved included differential and algebraic geometry, linear and commutative algebra, and functional and stochastic analysis.

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