On the selection of poles in the single-input pole placement problem Original Research Article

It is well known that the single-input pole placement problem can be quite sensitive to perturbations in the data. Recent results by Mehrmann and Xu show how this sensitivity depends on the location of the poles. In many applications it suffices to prescribe a set K in the complex plane that contains the poles. Mehrmann and Xu formulated a minimization problem for allocating the poles in a given set K so that the sensitivity to perturbations is reduced. The present paper uses methods of potential theory to derive simple algorithms that yield approximate solutions of this minimization problem.