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Arbitrary pole placement with the extended Kautsky-Nichols-van Dooren parametric form with minimum gain

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2014
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Conference Paper

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Schmid, R. and Nguyen, T. and Ntogramatzidis, L. 2014. Arbitrary pole placement with the extended Kautsky-Nichols-van Dooren parametric form with minimum gain, in Proceedings of the American Control Conference (ACC), Jun 4-6 2014, pp. 5663-5668. Portland, Oregon, USA: Institute of Electrical and Electronics Engineers Inc.
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Proceedings of the American Control Conference
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2014 American Control Conference (ACC)
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Department of Mathematics and Statistics
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NOTICE: This is the author’s version of a work in which changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication.

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Abstract

We consider the classic problem of pole placement by state feedback. We revisit the well-known eigenstructure assignment algorithm of Kautsky, Nichols and van Dooren [1] and extend it to obtain a novel parametric form for the pole-placing feedback matrix that can deliver any set of desired closed-loop eigenvalues, with any desired multiplicities. This parametric formula is then employed to introduce an unconstrained nonlinear optimisation algorithm to obtain a feedback matrix that delivers the desired pole placement with minimum gain.