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11:00 a.m.
Jeong H. Kim Building, Kay Boardrooms I&II
For More Information:
Peggy Johnson
301 405 6615
pjohnson@umd.edu
Abstract
We survey several aspects of an apparently simple (but so far unsolved) question: under what conditions on the matrices A and B do all possible infinite products of the type ABBABAAAB... converge to zero?
This question can be formalized by introducing the concept of joint spectral radius that measures the maximal asymptotic growth rate that can be obtained by forming long products of matrices taken from a set. The joint spectral radius appears in a number of application contexts but is notoriously difficult to compute and to approximate.
In this talk, we describe applications of the joint spectral radius in hybrid systems, wavelets, codes and sensor networks. We prove that the problem of determining if the set all possible products of two matrices is bounded, is algorithmically undecidable and we exhibit the occurrence of Sturmian sequences in the analysis of optimal periodic products. We conclude with a recent efficient approximation algorithm for the joint spectral radius. The algorithm approximates the joint spectral with arbitrary high accuracy and is polynomial in the size of the matrices once the desired accuracy is fixed.
Joint work with J. Tsitsiklis and Y. Nesterov.
Biography
Vincent D. Blondel received a Bachelor Degree in Engineering in Applied Mathematics from the University of Louvain (Louvain-la-Neuve, Belgium) in 1988, a Master Degree in Pure Mathematics from Imperial College (London, UK) and a Doctorate in 1992 from the University of Louvain.
In 1993, he was a visiting scientist at Oxford University. During the academic year 1993-1994, he was the Göran Gustafsson Fellow at the Royal Institute of Technology (Stockholm, Sweden). In 1993-1994 he was a research fellow at the French National Research Center in Control and Computer Science (INRIA, Rocquencourt-Paris). From 1994 to 1999 he was an associate professor at the Institute of Mathematics of the Université de Liège in Belgium. Since October 1999 he is with the University of Louvain where he is currently professor in the Department of Applied Mathematics. He has been a visitor with the Australian National University (1991), the University of California at Berkeley (1998), the Santa Fe Institute (2000), Harvard University (2001) and is visiting the Massachusetts Institute of Technology every year since 1994. He has also been an invited professor at the Ecole Normale Supérieure in Lyon (1998) and at the University of Paris VII (1999 and 2000).
Dr Blondel's major current research interests lie in several areas of mathematical control theory and theoretical computer science. He has been a recipient of a Grant from the Trustees of the Mathematics Institute of Oxford University (1992), the Prize Agathon De Potter of the Belgian Royal Academy of Science (1993) and the Prize Paul Dubois of the Montefiore Institute (1993). He is the coordinator of a NATO collaborative grant with the Massachusetts Institute of Technology (USA) and the Russian Academy of Science, and is a partner in a European TMR network on discrete event systems. He is a former associate editor of the European Journal of Control (Springer) and an associate editor of Systems and Control Letters (Elsevier) and of the Journal on Mathematics of Control, Signals, and Systems (Springer). He was awarded the triennal SIAM prize on control and systems theory in 2001.
Host
Nuno Martins, ECE/ISR, nmartins@isrmail.isr.umd.edu
This Event is For: Public • Clark School • Graduate • Faculty • Post-Docs • Alumni • Corporate
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