Robust eigenstructure assignment in quadratic matrix polynomials: Nonsingular case. (English) Zbl 0995.65069

Nichols, N. K.; Kautsky, J.

SIAM J. Matrix Anal. Appl. 23, No. 1, 77-102 (2001).

New sensitivity measures for the eigenvalues of a quadratic matrix polynomial are derived and a measure of the robustness of the corresponding second-order control system is defined. It is shown that the robustness of the associated 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 equired.
In this part of the work the authors treat the case where the leading coefficient matrix in the quadratic polynomial is nonsingular, which ensures that the polynomial is regular. Some low order examples are presented.

Reviewer: Petko Hr.Petkov (Sofia)

MSC:

65K10	Numerical optimization and variational techniques
93B55	Pole and zero placement problems
65F18	Numerical solutions to inverse eigenvalue problems
65F35	Numerical computation of matrix norms, conditioning, scaling
93B52	Feedback control
93B35	Sensitivity (robustness)

Keywords:

second-order control systems; quadratic inverse eigenvalue problem; feedback design; robust eigenstructure assignment; structured perturbations; numerical examples; sensitivity measures; quadratic matrix polynomial