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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

In this paper we relate the stability radius that can be achieved for the closed-loop matrix (ABK) to the distance to unstabilizability of the pair (A,B). In the paper we show that the closed-loop matrix (ABK) 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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Copyright © 2006 by American Society of Mechanical Engineers
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References

Figures

Grahic Jump Location
Figure 1

Variation of δus(A,βB) with β

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