We discuss the single-input pole placement problem (SIPP) and analyze how the conditioning of the problem can be estimated and improved if the poles are allowed to vary in specific regions in the complex plane. Under certain assumptions we give formulas as well as bounds for the norm of the feedback gain and the condition number of the closed loop matrix. Via several numerical examples we demonstrate how these results can be used to estimate the condition number of a given SIPP problem and also demonstrate how to select the poles to improve the conditioning.
This is the published version, also available here: http://dx.doi.org/10.1137/S0895479896302382.
Mehrmann, Volker & Xu, Hongguo. "Choosing Poles So That the Single-Input Pole Placement Problem Is Well Conditioned." SIAM. J. Matrix Anal. & Appl., 19(3), 664–681. (18 pages) 1998. http://dx.doi.org/10.1137/S0895479896302382.