Michael Overton
Stability Optimization for Polynomials and Matrices
Time: Friday, October 11th, 2013, 2:30 pm
Location: CEWIT 200

Suppose that the coefficients of a monic polynomial or entries of a square matrix depend affinely on parameters, and consider the problem of minimizing the root radius (maximum of the moduli of the roots) or root abscissa (maximum of their real parts) in the polynomial case and the spectral radius or spectral abscissa in the matrix case.

These functions are not convex and they are typically not locally Lipschitz near minimizers. We first address polynomials, for which some remarkable analytical results are available in one special case, and then consider the more general case of matrices, focusing on the static output feedback problem arising in control of linear dynamical systems. The polynomial results are joint with V. Blondel, M. Gurbuzbalaban and A. Megretski.