A new proof of Ackermann’s formula from control theory
DOI:
https://doi.org/10.24193/subbmath.2017.3.05Keywords:
Eigenvalues placement algorithms, rank one updates, linear systems, matrix determinants.Abstract
This paper presents a novel proof for the well known Ackermann’s formula, related to pole placement in linear time invariant systems. The proof uses a lemma [3], concerning rank one updates for matrices, often used to efficiently compute the determinants. The proof is given in great detail, but it can be summarised to few lines.
Mathematics Subject Classification (2010): 26D10, 46N30.
References
Ackermann, J., Der Entwurf linearer Regelungsysteme im Zustandraum, Regeltech. Proz.-Datenverarb., 7(1972), 297-300.
Bass, W., Gura, I., High order system design via state-space considerations, Preprints, Join Automatic Control Conference, Rensselner Polytechnic Institute, Troy, N.Y., 1965, 311-318.
Ding, J., Zhou, A., Eigenvalues of rank-one updated matrices with some applications, Appl. Math. Lett., 20(2007), 1223-1226.
Ogata, K., Modern Control Engineering, 4th Ed. Englewood Cliffs, NJ, Prentice Hall, 2001.
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