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A regular matrix pencil sE-A and its rank one perturbations are considered.We determine the sets in the extended complex plane which are the eigenvaluesof the perturbed pencil. We show that the largest Jordan chains at eacheigenvalue of sE-A may disappear and the sum of the length of all destroyedJordan chains is the number of eigenvalues (counted with multiplicities) whichcan be placed arbitrarily in the extended complex plane. We prove sharp upperand lower bounds of the change of the algebraic and geometric multiplicity ofan eigenvalue under rank one perturbations. Finally we apply our results to apole placement problem for a single-input differential algebraic equation withfeedback.

Eigenvalue placement for regular matrix pencils with rank one perturbations