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Robust matrix đ U âstability analysis
Author(s) -
Bachelier O.,
Mehdi D.
Publication year - 2003
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/rnc.736
Subject(s) - cluster analysis , robustness (evolution) , upper and lower bounds , polytope , disjoint sets , matrix (chemical analysis) , mathematics , mathematical optimization , robust control , symmetric matrix , computer science , combinatorics , artificial intelligence , eigenvalues and eigenvectors , control system , engineering , mathematical analysis , biochemistry , chemistry , materials science , physics , quantum mechanics , composite material , gene , electrical engineering
In this paper, the problem of robust matrix rootâclustering is addressed. The studied matrices are subject to both polytopic and unstructured uncertainties. An original point is the large choice of clustering regions enabled by the proposed approach since these regions can be unions of possibly disjoint and nonâsymmetric subregions of the complex plane. The precise purpose is, considering a specified polytope, to determine the greatest robustness bound on the unstructured uncertainty such that robust matrix rootâclustering is ensured. To reduce conservatism in the derivation of the bound, the reasoning relies on a framework based upon parameterâdependent Lyapunov functions. The bound value is computed by solving an â âł â problem. Copyright © 2003 John Wiley & Sons, Ltd.