15 May 2003

14:00

Prof Nancy Nichols

Abstract

Feedback design for a second order control system leads to an
eigenstructure assignment problem for a quadratic matrix polynomial. It is
desirable that the feedback controller not only assigns specified
eigenvalues to the second order closed loop system, but also that the
system is robust, or insensitive to perturbations. We derive here new
sensitivity measures, or condition numbers, for the eigenvalues of the
quadratic matrix polynomial and define a measure of robustness of the
corresponding system. We then show that the robustness of the quadratic
inverse eigenvalue problem can be achieved by solving a generalized linear
eigenvalue assignment problem subject to structured perturbations.
Numerically reliable methods for solving the structured generalized linear
problem are developed that take advantage of the special properties of the
system in order to minimize the computational work required.