2016•arXiv (Cornell University)Open access
Eigenvalue placement for regular matrix pencils with rank one\n perturbations
Hannes Gernandt, Carsten Trunk
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Abstract
A regular matrix pencil sE-A and its rank one perturbations are considered.\nWe determine the sets in the extended complex plane which are the eigenvalues\nof the perturbed pencil. We show that the largest Jordan chains at each\neigenvalue of sE-A may disappear and the sum of the length of all destroyed\nJordan chains is the number of eigenvalues (counted with multiplicities) which\ncan be placed arbitrarily in the extended complex plane. We prove sharp upper\nand lower bounds of the change of the algebraic and geometric multiplicity of\nan eigenvalue under rank one perturbations. Finally we apply our results to a\npole placement problem for a single-input differential algebraic equation with\nfeedback.\n
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