Optimization and Pole Assignment in Control System Design

Some elementary optimization techniques, together with some not so well-known robustness measures and condition numbers, will be utilized in pole assignment. In particular, "Method 0" by Kautsky et al. (1985) for optimal selection of vectors is shown to be convergent to a local minimum, with respect to the condition number 1/2 ||X||_F^2 - ln |det X|. This contrasts with the misconception by Kautsky et al. that the method diverges, or the recent discovery by Yang and Tits (1995) that the method converges to stationary points.