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

Authors:
Tie-xiang Li;Eric King-wah Chu;Wen-Wei Lin
Affiliations:
Department of Mathematics, Southeast University, Nanjing, 211189, People's Republic of China;School of Mathematical Sciences, Building 28, Monash University, VIC 3800, Australia;Department of Applied Mathematics, National Chiao Tung University, Hsinchu 300, Taiwan
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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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 on 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.