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

Marius Simion Costandin, Petru Dobra, Bogdan Gavrea

Abstract


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.


Keywords


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

Full Text:

PDF

References


Jiu Ding, Aihui Zhou Eigenvalues of rank-one updated matrices with some

applications Applied Mathematics Letters 20 (2007) 1223-1226

Ackermann J., Der Entwurf linearer Regelungsysteme im Zustandraum Regel-

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




DOI: http://dx.doi.org/10.24193/subbmath.2017.3.05

Refbacks

  • There are currently no refbacks.