Open Problems in Mathematical Systems and Control Theory

by Blondel, Vincent D.; Sontag, Eduardo D.; Vidyasagar, M.; Willems, Jan C.

• ISBN13: 9781852330446
• ISBN10: 1852330449
• Edition: 1st
• Format: Hardcover
• Copyright: 1999-10-01
• Publisher: Springer Verlag

Summary

This 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.

Table of Contents

Uniform asymptotic stability of linear time-varying systems	1	(6)
Dirk Aeyels
Joan Peuteman
Positive system realizations	7	(4)
Brian D. O. Anderson
System approximation in the 2-norm	11	(4)
A. C. Antoulas
Is it possible to recognize local controllability in a finite number of differentiations?	15	(4)
Andrei A. Agrachev
Open problems in sequential parametric estimation	19	(4)
Er-Wei Bai
Roberto Tempo
Yinyu Ye
Conditions for the existence and uniqueness of optimal matrix scalings	23	(4)
Venkataramanan Balakrishnan
Matrix inequality conditions for canonical factorization of rational transfer function matrices	27	(4)
Venkataramanan Balakrishnan
Open problems in l1 optimal control	31	(4)
Bassam Bamieh
Munther A. Dahleh
Efficient neural network learning	35	(4)
Peter L. Bartlett
Mechanical feedback control systems	39	(6)
Anthony M. Bloch
Naomi Ehrich Leonard
Jerrold E. Marsden
Three problems on the decidability and complexity of stability	45	(8)
Vincent D. Blondel
John N. Tsitsiklis
Simultaneous stabilization of linear systems and interpolation with rational functions	53	(8)
Vincent D. Blondel
Forbidden state control synthesis for timed Petri net models	61	(6)
R. K. Boel
G. Stremersch
On matrix mortality in low dimensions	67	(4)
Olivier Bournez
Michael Branicky
Entropy and random feedback	71	(4)
Stephen P. Boyd
A stabilization problem	75	(4)
Roger Brockett
Spectral factorization of a spectral density with arbitrary delays	79	(4)
Frank M. Callier
Joseph J. Winkin
Lyapunov exponents and robust stabilization	83	(6)
F. Colonius
D. Hinrichsen
F. Wirth
Regular spectral factorizations	89	(6)
Ruth F. Curtain
Olof J. Staffans
Convergence of an algorithm for the Riemannian SVD	95	(4)
Bart De Moor
Some open questions related to flat nonlinear systems	99	(6)
Michel Fliess
Jean Levine
Philippe Martin
Pierre Rouchon
Approximation of complex μ	105	(4)
Minyue Fu
Spectral value sets of infinite-dimensional systems	109	(6)
E. Gallestey
D. Hinrichsen
A. J. Pritchard
Selection of the number of inputs and states	115	(6)
Christiaan Heij
Input-output gains of switched linear systems	121	(4)
J. P. Hespanha
A. S. Morse
Robust stability of linear stochastic systems	125	(6)
D. Hinrichsen
A. J. Pritchard
Monotonicity of performance with respect to its specification in H∞ control	131	(6)
Hidenori Kimura
Stable estimates in equation error identification: An open problem	137	(4)
Roberto Lopez-Valcarce
Soura Dasgupta
Elimination of latent variables in real differential algebraic systems	141	(8)
Iven Mareels
Jan C. Willems
How conservative is the circle criterion?	149	(4)
Alexandre Megretski
On chaotic observer design	153	(4)
Henk Nijmeijer
The minimal realization problem in the max-plus algebra	157	(6)
Geert Jan Olsder
Bart De Schutter
Input design for worst-case identification	163	(4)
Jonathan R. Partington
Max-plus-times linear systems	167	(4)
Max Plus
Closed-loop identification and self-tuning	171	(6)
Jan Willem Polderman
To estimate the L2-gain of two dynamic systems	177	(4)
Anders Rantzer
Open problems in the area of pole placement	181	(12)
Joachim Rosenthal
Jan C. Willems
An optimal control theory for systems defined over finite rings	193	(10)
Joachim Rosenthal
Re-initialization in discontinuous systems	203	(8)
J. M. Schumacher
Control-Lyapunov functions	211	(6)
Eduardo D. Sontag
Spectral Nevanlinna-Pick Interpolation	217	(4)
Allen R. Tannenbaum
Phase-sensitive structured singular value	221	(4)
Andre L. Tits
V. Balakrishnan
Conservatism of the standard upper bound test: Is sup(μ/μ) finite? Is it bounded by 2?	225	(4)
Onur Toker
Bram de Jager
When does the algebraic Riccati equation have a negative semi-definite solution?	229	(10)
Harry L. Trentelman
Representing a nonlinear input-output differential equation as an input-state-output system	239	(6)
A. J. van der Schaft
Shift policies in QR-like algorithms and feedback control of self-similar flows	245	(6)
Paul Van Dooren
Rodolphe Sepulchre
Equivalences of discrete-event systems and of hybrid systems	251	(8)
J. H. van Schuppen
Covering numbers for input-output maps realizable by neural networks	259	(8)
M. Vidyasagar
A powerful generalization of the Carleson measure theorem?	267	(6)
George Weiss
Lyapunov theory for high order differential systems	273	(4)
Jan C. Willems
Performance lower bound for a sampled-data signal reconstruction	277	(4)
Yutaka Yamamoto
Shinji Hara
Coprimeness of factorizations over a ring of distributions	281	(4)
Yutaka Yamamoto
Where are the zeros located?	285	(4)
Hans Zwart
Index	289