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On relationship between quadratic and robust stability of uncertain systems
Author(s) -
Chen WenHua
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(199901)9:1<51::aid-rnc393>3.0.co;2-a
Subject(s) - quadratic equation , stability (learning theory) , equivalence (formal languages) , bounded function , mathematics , mathematical optimization , regular polygon , robustness (evolution) , convex optimization , computer science , discrete mathematics , mathematical analysis , biochemistry , chemistry , geometry , machine learning , gene
A game theoretic approach is introduced to analyse the relationship between the quadratic and robust stability of systems with structured uncertainties. Necessary and sufficient condition for the equivalence of these two types of stability is presented. The distance between quadratic and robust stability is bounded when this condition is not satisfied. This gives new insight into the mechanism of the quadratic stability. Checking this necessary and sufficient condition and calculating the error bound are formulated as a convex optimization problem. The results developed in this paper are illustrated by several numerical examples. Copyright © 1999 John Wiley & Sons, Ltd.