Comments, with reply, on "Computational algorithms for pole assignment" by N.K. Nichols

Petkov, P.H., Christov, N.D., Konstantinov, M.M. and Nichols, N. ORCID: https://orcid.org/0000-0003-1133-5220 (1988) Comments, with reply, on "Computational algorithms for pole assignment" by N.K. Nichols. IEEE Transactions on Automatic Control, 33 (9). pp. 892-894. ISSN 0018-9286 doi: 10.1109/9.1328

Abstract/Summary

Some points of the paper by N.K. Nichols (see ibid., vol.AC-31, p.643-5, 1986), concerning the robust pole assignment of linear multiinput systems, are clarified. It is stressed that the minimization of the condition number of the closed-loop eigenvector matrix does not necessarily lead to robustness of the pole assignment. It is shown why the computational method, which Nichols claims is robust, is in fact numerically unstable with respect to the determination of the gain matrix. In replying, Nichols presents arguments to support the choice of the conditioning of the closed-loop poles as a measure of robustness and to show that the methods of J Kautsky, N. K. Nichols and P. VanDooren (1985) are stable in the sense that they produce accurate solutions to well-conditioned problems.