"This is an extremely important book that presents, in a clear way, many important and stimulating mathematical problems in systems and control. It will be an important reference for both researchers and people outside the field."--William W. Hager, University of Florida

This book provides clear presentations of more than sixty important unsolved problems in mathematical systems and control theory. Each of the problems included here is proposed by a leading expert and set forth in an accessible manner. Covering a wide range of areas, the book will be an ideal reference for anyone interested in the latest developments in the field, including specialists in applied mathematics, engineering, and computer science.

The book consists of ten parts representing various problem areas, and each chapter sets forth a different problem presented by a researcher in the particular area and in the same way: description of the problem, motivation and history, available results, and bibliography. It aims not only to encourage work on the included problems but also to suggest new ones and generate fresh research. The reader will be able to submit solutions for possible inclusion on an online version of the book to be updated quarterly on the Princeton University Press website, and thus also be able to access solutions, updated information, and partial solutions as they are developed.

Download Unsolved Problems in Mathematical Systems and Control Theory

PDF version, 1.4MB, 350Pages.

Edited by Vincent D. Blondel and Alexandre Megretski.

Copyright 2004 by Princeton University Press.

Unsolved Problems in Mathematical Systems and Control Theory Official Website

Preface: Five years ago, a first volume of open problems in Mathematical Systems and Control Theory appeared. Some of the 53 problems that were published in this volume attracted considerable attention in the research community. The book in front of you contains a new collection of 63 open problems. The contents of both volumes show the evolution of the field in the half decade since the publication of the first volume. One noticeable feature is the shift toward a wider class of questions and more emphasis on issues driven by physical modeling.

Early versions of some of the problems in this book have been presented at the Open Problem sessions of the Oberwolfach Tagung on Regelungstheorie, on February 27, 2002, and of the Conference on Mathematical Theory of Networks and Systems (MTNS) in Notre Dame, Indiana, on August 12, 2002.

The editors thank the organizers of these meetings for their willingness to provide the problems this welcome exposure.

Since the appearance of the first volume, open problems have continued to meet with large interest in the mathematical community. Undoubtedly, the most spectacular event in this arena was the announcement by the Clay Mathematics Institute of the Millennium Prize Problems whose solution will be rewarded by one million U.S. dollars each. Modesty and modesty of means have prevented the editors of the present volume from offering similar rewards toward the solution of the problems in this book. However, we trust that, notwithstanding this absence of a financial incentive, the intellectual challenge will stimulate many readers to attack the problems.

The editors thank in the first place the researchers who have submitted the problems. We are also very thankful to the Princeton University Press, and in particular Vickie Kearn, for their willingness to publish this volume.

The full text of the problems, together with comments, additions, and solutions, will be posted on the book website at Princeton University Press (link available from http://pup.princeton.edu/math/) and on http://www.inma.ucl.ac.be/blondel/op/. Readers are encouraged to submit contributions by following the instructions given on these websites.

The editors, Louvain-la-Neuve, March 15, 2003.

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