The formulation and numerical method for partial quadratic eigenvalue assignment problems

Abstract

In this paper, we consider the minimum norm and robust partial quadratic eigenvalue assignment problems (PQEVAP). A complete theory on the existence of solutions for the PQEVAP is established. It is shown that solving the PQEVAP is essentially solving an eigenvalue assignment for a linear system of a much lower order, and the minimum norm and robust PQEVAPs are then concerning the minimum norm and robust eigenvalue assignment problems associated with this linear system. Based on this theory, an algorithm for solving the minimum norm and robust PQEVAPs is proposed, and its efficient behaviors are illustrated by some numerical examples. Copyright © 2010 John Wiley & Sons, Ltd.