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One of the standard problems in controller design of linear systems is the so-called pole placement problem. Although there are meanwhile a couple of algorithms for this problem on the market, the most common approach (at least for single—input systems) is the one suggested by Jilrgen Acl< ermann ‘-As it was recently shown by Alan Laub er a//a 2, this algorithm is numerically harmful. For systems of larger than lO “‘order, double precision is required on a 32-bit machine (eg VAX); for systems larger than about lS “‘order, the algorithm fails altogether. Newer algorithms making use of a numerically more stable transformation (eg Hessenberg form) are behaving better, but were shown to fail as well for systems of larger than approximately 20"‘to 25"‘order. The authors therefore suggested (without proof) that the pole placement problem is intrinsically ill—posed. in this paper, we present an algorithm which shows …