On computation of the stability radius for nonlinearly structured perturbations |
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Authors: | Wei-Yong Yan James Lam |
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Affiliation: | aSchool of Electrical and Computer Engineering, Curtin University of Technology, GPO Box U1987, Perth 6845, Australia;bDepartment of Mechanical Engineering, University of Hong Kong, Pokfulam Road, Hong Kong |
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Abstract: | This paper considers the problem of finding a perturbation matrix with the least spectral norm such that a matrix-valued function becomes singular, where the dependence of the function on the perturbation is allowed to be nonlinear. It is proved that such a problem can be approximated by a smooth unconstrained minimization problem with compact sublevel sets. A computational procedure proposed based on this result is demonstrated to be effective in both linear and nonlinear cases. |
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Keywords: | Linear systems Stability radius Robustness Gradient flow Matrix analysis |
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