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
Jiu Ding, Aihui Zhou Eigenvalues of rank-one updated matrices with some
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tech. Proz.-Datenverarb.,7,pp.297-300,1972
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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