Robust arbitrary pole placement with the extended Kautsky-Nichols-van Dooren parametric form

Abstract

We consider the classic problem of pole placement by state feedback. Our recent work [1] offered an eigenstructure assignment algorithm to obtain a novel parametric form for the pole-placing gain matrix to deliver any set of desired closed-loop eigenvalues, with any desired multiplicities. The method was adapted from the classic eigenstructure assignment algorithm of Kautsky, Nichols and van Dooren [2]. In this paper we employ this parametric formula to introduce an unconstrained nonlinear optimisation algorithm to obtain a gain matrix that delivers any desired pole placement with optimal robustness.

Arbitrary pole placement with the extended Kautsky–Nichols–van Dooren parametric form

“…Unconstrained nonlinear optimisation methods can then be used to seek local minima. Computation of the matrix derivatives required for κ FRO (X) appeared in (Schmid et al, 2014b), and the matrix derivatives required for F K 2 appeared in (Schmid et al, 2014c).…”