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A new proof of Ackerman’s formula from control theory. (English) Zbl 1413.93041
Summary: 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 J. Ding and A. Zhou [Appl. Math. Lett. 20, No. 12, 1223–1226 (2007; Zbl 1139.15003)], 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.
93B55 Pole and zero placement problems
93B51 Design techniques (robust design, computer-aided design, etc.)
93C05 Linear systems in control theory
93B60 Eigenvalue problems
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