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

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.