A structure-preserving doubling algorithm for quadratic eigenvalue problems arising from time-delay systems

Abstract

We propose a structure-preserving doubling algorithm for a quadratic eigenvalue problem arising from the stability analysis of time-delay systems. We are particularly interested in the eigenvalues oil the unit circle, which are difficult to estimate. The convergence and backward error of the algorithm are analyzed and three numerical examples are presented. Our experience shows that Our algorithm is efficient in comparison to the few existing approaches for small to medium size problems. (C) 2009 Elsevier B.V. All rights reserved.