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

#### 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

#### 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-

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Ogata K., Modern Control Engineering, 4th Ed Englewood Clis, NJ, Prentice

Hall, 2001

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

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