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Open Problems in Mathematical Systems and Control Theory

  • Book
  • © 1999

Overview

Editors:
  1. Vincent Blondel

    1. Institute of Mathematics, University of Leige, Liege, Belgium

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  2. Eduardo D. Sontag

    1. Department of Mathematics, Rutgers University, New Brunswick, USA

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  3. Mathukumalli Vidyasagar

    1. Centre for Arificial Intelligence and Robotics, Bangalore, India

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  4. Jan C. Willems

    1. Institute of Mathematics, Rijksuniversiteit te Groningen, Av Groningen, The Netherlands

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  • Over fifty open problems presented, explained and discussed by leading researchers in the field
  • Is designed to generate further discussion on these problems, and others that it inspires
  • System and control theory is one of the most exciting areas of contemporary engineering mathematics

Part of the book series: Communications and Control Engineering (CCE)

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Table of contents (53 chapters)

  1. Front Matter

    Pages i-xii
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  2. Uniform asymptotic stability of linear time-varying systems

    • Dirk Aeyels, Joan Peuteman
    Pages 1-5

  3. Positive system realizations

    • Brian D. O. Anderson
    Pages 7-10

  4. System approximation in the 2-norm

    • A. C. Antoulas
    Pages 11-14

  5. Is it possible to recognize local controllability in a finite number of differentiations?

    • Andrei A. Agrachev
    Pages 15-18

  6. Open problems in sequential parametric estimation

    • Er-Wei Bai, Roberto Tempo, Yinyu Ye
    Pages 19-22

  7. Conditions for the existence and uniqueness of optimal matrix scalings

    • Venkataramanan Balakrishnan
    Pages 23-25

  8. Matrix inequality conditions for canonical factorization of rational transfer function matrices

    • Venkataramanan Balakrishnan
    Pages 27-29

  9. Open problems in ℓ 1 optimal control

    • Bassam Bamieh, Munther A. Dahleh
    Pages 31-33

  10. Efficient neural network learning

    • Peter L. Bartlett
    Pages 35-38

  11. Mechanical feedback control systems

    • Anthony M. Bloch, Naomi Ehrich Leonard, Jerrold E. Marsden
    Pages 39-44

  12. Three problems on the decidability and complexity of stability

    • Vincent D. Blondel, John N. Tsitsiklis
    Pages 45-51

  13. Simultaneous stabilization of linear systems and interpolation with rational functions

    • Vincent D. Blondel
    Pages 53-59

  14. Forbidden state control synthesis for timed Petri net models

    • R. K. Boel, G. Stremersch
    Pages 61-66

  15. On matrix mortality in low dimensions

    • Olivier Bournez, Michael Branicky
    Pages 67-69

  16. Entropy and random feedback

    • Stephen P. Boyd
    Pages 71-74

  17. A stabilization problem

    • Roger Brockett
    Pages 75-78

  18. Spectral factorization of a spectral density with arbitrary delays

    • Frank M. Callier, Joseph J. Winkin
    Pages 79-82

  19. Lyapunov exponents and robust stabilization

    • F. Colonius, D. Hinrichsen, F. Wirth
    Pages 83-88

  20. Regular spectral factorizations

    • Ruth F. Curtain, Olof J. Staffans
    Pages 89-93
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Keywords

About this book

System and Control theory is one of the most exciting areas of contemporary engineering mathematics. From the analysis of Watt's steam engine governor - which enabled the Industrial Revolution - to the design of controllers for consumer items, chemical plants and modern aircraft, the area has always drawn from a broad range of tools. It has provided many challenges and possibilities for interaction between engineering and established areas of 'pure' and 'applied' mathematics. This impressive volume collects a discussion of more than fifty open problems which touch upon a variety of subfields, including: chaotic observers, nonlinear local controlability, discrete event and hybrid systems, neural network learning, matrix inequalities, Lyapunov exponents, and many other issues. Proposed and explained by leading researchers, they are offered with the intention of generating further work, as well as inspiration for many other similar problems which may naturally arise from them. With extensive references, this book will be a useful reference source - as well as an excellent addendum to the textbooks in the area.

Editors and Affiliations

  • Institute of Mathematics, University of Leige, Liege, Belgium

    Vincent Blondel

  • Department of Mathematics, Rutgers University, New Brunswick, USA

    Eduardo D. Sontag

  • Centre for Arificial Intelligence and Robotics, Bangalore, India

    Mathukumalli Vidyasagar

  • Institute of Mathematics, Rijksuniversiteit te Groningen, Av Groningen, The Netherlands

    Jan C. Willems

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