### Saturday, September 23

## MS34

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