An application of the matrix determinant lemma in the theory of control

Marius Simion Costandin, Petru Dobra, Bogdan Gavrea


This paper presents a novel proof for the well known Ack-
ermann's formula, related to pole placement in linear time invariant
systems. The proof uses a lemma [1], concerning rank one updates for
matrices, often used to eciently compute the determinants. The proof
is given in great detail, but it can be summarised to few lines.


eigenvalues placement algorithms; rank one updates; linear systems, matrix determinants

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