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TECHNICAL BRIEFS

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

[+] Author and Article Information
R. Rajamani

Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455rajamani@me.umn.edu

Y. M. Cho1

School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-742, Koreaymcho85@snu.ac.kr

1

Corresponding author.

J. Dyn. Sys., Meas., Control 128(3), 718-721 (Oct 02, 2005) (4 pages) doi:10.1115/1.2234490 History: Received April 02, 2004; Revised October 02, 2005

## 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.

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## Figures

Figure 1

Variation of δus(A,βB) with β

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