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Rank Stability Radius for a Matrix with Structured Scalar Perturbations

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Open access
Authors
Xing, W.
Yan, W.
Liu, Wan-quan
Date
2009
Type
Conference Paper

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Citation
Xing, W. and Yan, W. and Liu, Wan-quan. 2009. Rank Stability Radius for a Matrix with Structured Scalar Perturbations, in Bailliul, J. and Gua, L. (ed), 48th CDC/28th CCC 09, Dec 16 2009, pp. 6160-6165. Shanghai, P.R. China: IEEE.
Source Title
Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference,
Source Conference
48th CDC/28th CCC 09
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Department of Electrical and Computer Engineering
School of Engineering
Faculty of Science and Engineering
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Abstract

In this paper, the rank stability radius problem is proposed for a real matrix under structured scalar perturbations and some interesting results are achieved based on polynomial analysis. In addition, a computable formula and a two-step procedure are obtained which nicely solves the problem in this simple set up. Finally, these results on rank stability radius are used to estimate the stability robustness of descriptor systems, and for a special class of symmetric descriptor systems, the rank stability radius is proved to be equal to the system stability radius.