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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.
MSC:
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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