Saturday, September 23

Optimizing Matrix Stability

10:30 AM-12:30 PM
New Hampshire 1

Stability is a key desirable feature of dynamical systems, and when systems have degrees of freedom, it is natural to try to optimize stability in some sense. Exactly what this means depends on the application and the model. The simplest model is: minimize the spectral abscissa (maximum real part of the eigenvalues) or the spectral radius of the parameter dependent matrix representing the system. Even when the matrices in question depend linearly on the parameters, these problems are known to be hard to solve, indeed NP hard in certain contexts. Yet such problems are crucial in control theory, for example: here a basic model is the static output feedback problem: given A,B,C find X for which the matrix A + BXC is stable.

Organizer: Michael L. Overton
Courant Institute of Mathematical Sciences, New York University, USA
10:30-10:55 Algorithms for Optimizing Matrix Stability
James V. Burke, University of Washington, USA; Adrian S. Lewis, University of Waterloo, Canada; and Michael L. Overton, Organizer
11:00-11:25 Title to be determined
John Doyle, California Institute of Technology, USA
11:30-11:55 Relaxations in Non-Convex Quadratic Optimization and Feedback Stabilization
Alexandre Megretski, Massachusetts Institute of Technology, USA
12:00-12:25 Subdivision Filter Design and Spectral Radius Optimization
Thomas P.-Y. Yu, Rensselaer Polytechnic Institute, USA

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Created 6/14/00; Updated 6/14/00