An application of the matrix determinant lemma in the theory of control
DOI:
https://doi.org/10.24193/subbmath.2017.3.05Keywords:
eigenvalues placement algorithms, rank one updates, linear systems, matrix determinantsAbstract
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.
References
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Ogata K., Modern Control Engineering, 4th Ed Englewood Clis, NJ, Prentice
Hall, 2001
W. Bass, I. Gura High order system design via state-space considerations Preprints, 1965 Join Automatic Control Conference, pp. 311-318, Rensselner Polytechnic Institute, Troy, N.Y., June 22-25
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