Accessibility navigation


Robust eigenstructure assignment in quadratic matrix polynomials: nonsingular case

Nichols, N.K. and Kautsky, J. (2001) Robust eigenstructure assignment in quadratic matrix polynomials: nonsingular case. SIAM Journal on Matrix Analysis and Applications, 23 (1). pp. 77-102. ISSN 0895-4798

Full text not archived in this repository.

To link to this article DOI: 10.1137/S0895479899362867

Abstract/Summary

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 the 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. In this part of the work we treat the case where the leading coefficient matrix in the quadratic polynomial is nonsingular, which ensures that the polynomial is regular. In a second part, we will examine the case where the open loop matrix polynomial is not necessarily regular.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical and Physical Sciences > Department of Meteorology
Faculty of Science > School of Mathematical and Physical Sciences > Department of Mathematics and Statistics
ID Code:27520
Uncontrolled Keywords:second-order control systems, quadratic inverse eigenvalue problem, feedback design, robust eigenstructure assignment, structured perturbations
Publisher:SIAM

Centaur Editors: Update this record

Page navigation