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Bounds for uncertain matrix root‐clustering in a union of subregions
Author(s) -
Bachelier O.,
Pradin B.
Publication year - 1999
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/(sici)1099-1239(199905)9:6<333::aid-rnc408>3.0.co;2-7
Subject(s) - root (linguistics) , matrix (chemical analysis) , cluster analysis , mathematics , statistics , philosophy , chemistry , linguistics , chromatography
The research for robustness bounds for systems whose behaviour is described by a linear state‐space model is addressed. The paper lays stress on the location of the eigenvalues of the state matrix when this matrix is subject either to an unstructured additive uncertainty or to a structured additive uncertainty . In the first case, upper bounds on the spectral norm of the uncertainty matrix are determined whereas in the second case, upper bounds on the maximal real perturbation in the state matrix are derived. In both cases, the fact that these bounds are not exceeded ensures that the eigenvalues of the uncertain state matrix lie in a specified region of the complex plane in which those of the nominal state matrix already lie. These bounds are obtained through a linear matrix inequalities approach. This approach allows to specify , not only as a simple convex region , symmetric with respect to the real axis, but also as a non‐convex (but symmetric with respect to the real axis) region defined itself as a union of convex subregions , each of them being not necessarily symmetric with respect to the real axis. Copyright © 1999 John Wiley & Sons, Ltd.