An Upper Bound on the Maximum Stability Radius Achievable by State Feedback

Abstract

In this paper we relate the stability radius that can be achieved for the closed-loop matrix (A−BK) to the distance to unstabilizability of the pair (A,B). In the paper we show that the closed-loop matrix (A−BK) can achieve a stability radius of γ with a real feedback matrix K only if the distance to unstabilizability of (A,B) is greater than γ. Thus the distance to the unstabilizability of (A,B) provides an upper bound on the maximum stability radius that can be achieved by state feedback.