Volume 4, pp. 89-105, 1996.

An analysis of the pole placement problem. I. The single-input case

Volker Mehrmann and Hongguo Xu


For the solution of the single-input pole placement problem we derive explicit expressions for the feedback gain matrix as well as the eigenvector matrix of the closed-loop system. Based on these formulas we study the conditioning of the pole-placement problem in terms of perturbations in the data and show how the conditioning depends on the condition number of the closed loop eigenvector matrix, which is a similar to a generalized Cauchy matrix, the norm of the feedback vector and the distance to uncontrollability.

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Key words

pole placement, condition number, perturbation theory, Jordan form, explicit formulas, Cauchy matrix, stabilization, feedback gain, distance to uncontrollability.

AMS subject classifications

65F15, 65F35, 65G05, 93B05, 93B55.

ETNA articles which cite this article

Vol. 5 (1997), pp. 77-97 Volker Mehrmann and Hongguo Xu: An analysis of the pole placement problem II. The multi-input case
Vol. 11 (2000), pp. 25-42 M. E. Cawood and C. L. Cox: Perturbation analysis for eigenstructure assignment of linear multi-input systems
Vol. 20 (2005), pp. 50-63 Daniel Kressner: On the use of larger bulges in the QR algorithm
Vol. 54 (2021), pp. 128-149 Sk. Safique Ahmad, Istkhar Ali, and Ivan Slapničar: Perturbation analysis of matrices over a quaternion division algebra

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