Open Problems in Mathematical Systems and Control Theory

1. Convergence of an algorithm for the Riemannian SVD

   • Bart De Moor

   Pages 95-98

2. Some open questions related to flat nonlinear systems

   • Michel Fliess, Jean Lévine, Philippe Martin, Pierre Rouchon

   Pages 99-103

3. Approximation of complex µ

   • Minyue Fu

   Pages 105-107

4. Spectral value sets of infinite-dimensional systems

   • E. Gallestey, D. Hinrichsen, A. J. Pritchard

   Pages 109-113

5. Selection of the number of inputs and states

   • Christiaan Heij

   Pages 115-119

6. Input-output gains of switched linear systems

   • J. P. Hespanha, A. S. Morse

   Pages 121-124

7. Robust stability of linear stochastic systems

   • D. Hinrichsen, A. J. Pritchard

   Pages 125-129

8. Monotonicity of performance with respect to its specification in H ^∞ control

   • Hidenori Kimura

   Pages 131-136

9. Stable estimates in equation error identification: An open problem

   • Roberto López-Valcarce, Soura Dasgupta

   Pages 137-140

10. Elimination of latent variables in real differential algebraic systems

    • Iven Mareels, Jan C. Willems

    Pages 141-147

11. How conservative is the circle criterion?

    • Alexandre Megretski

    Pages 149-151

12. On chaotic observer design

    • Henk Nijmeijer

    Pages 153-156

13. The minimal realization problem in the max-plus algebra

    • Geert Jan Olsder, Bart De Schutter

    Pages 157-162

14. Input design for worst-case identification

    • Jonathan R. Partington

    Pages 163-166

15. Max-plus-times linear systems

    • Max Plus

    Pages 167-170

16. Closed-loop identification and self-tuning

    • Jan Willem Polderman

    Pages 171-176

17. To estimate the L ₂-gain of two dynamic systems

    • Anders Rantzer

    Pages 177-179

18. Open problems in the area of pole placement

    • Joachim Rosenthal, Jan C. Willems

    Pages 181-191

19. An optimal control theory for systems defined over finite rings

    • Joachim Rosenthal

    Pages 193-201

20. Re-initialization in discontinuous systems

    • J. M. Schumacher

    Pages 203-209

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.

• Petri net
• chemical plants
• control
• control system
• control theory
• design
• feedback
• hybrid systems
• neural networks
• nonlinear system
• optimal control
• research
• scaling
• stability
• stabilization

• 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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