Eigenvalue Placement by Quantifier Elimination - the Static Output Feedback Problem

Abstract

This contribution addresses the static output feedback problem of linear time-invariant systems. This is still an area of active research, in contrast to the observer-based state feedback problem, which has been solved decades ago. We consider the formulation and solution of static output feedback design problems using quantifier elimination techniques. Stabilization, as well as more specified eigenvalue placement scenarios, are the focus of the paper.

Full and Partial Eigenvalue Placement for Minimum Norm Static Output Feedback Control

“…The optimal gain w.r.t. the Frobenius norm yields almost the same result as in case of for the minimum spectral norm achieving a small system norm (28). The K 1 -optimal gain matrix yields the largest system magnitude.…”

“…see [26]- [28]. Similar conditions can be derived for the stability with purely real eigenvalues, i.e., with roots on the open left half real axis, see [28]- [31].…”

“…The supremum over of the magnitude over all frequencies is the system norm (28). The results are listed in the last column of Table I.…”

“…It was shown [5] that system (67) is stabilizable by static output feedback, but a feedback matrix was not presented. The stabilization of this system is also discussed in [28].…”