The algebraic structure of pencils and block Toeplitz matrices
The paper restates several results on the Kronecker structure obtainable after a given matrix pencil is affected by an arbitrarily small perturbation, and states some new results on the Kronecker structure after a new row is appended or a column deleted. The results are simple consequences of a theory of majorization for semi-infinite integer sequences. The bounds after a new row is appended correspond to bounding the controllability indices after adding a single input to a linear time-invariant dynamical system. The known relations between the Kronecker indices, the Segre characteristics, and the nullities of certain block Toeplitz matrices constructed from the original pencils are illustrated. How those nullities change when the pencil is affected by a perturbation or a new row is also discussed.
majorization for semi-infinite integer sequences
scientific article; zbMATH DE number 1355352
scientific article