15 May 2003
Prof Nancy Nichols
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.
- Computational Mathematics and Applications Seminar