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Absolute stability of nonlinear systems with disc and norm‐bounded perturbations
Author(s) -
Impram Serkan T.,
Munro Neil
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.876
Subject(s) - norm (philosophy) , bounded function , nonlinear system , mathematics , salient , circle criterion , control theory (sociology) , stability (learning theory) , computer science , exponential stability , mathematical analysis , law , control (management) , physics , quantum mechanics , artificial intelligence , machine learning , political science
Abstract Absolute stability of uncertain nonlinear systems is studied using the celebrated Popov and circle criteria. Uncertainty is assumed to exist in terms of disc and norm‐bounded perturbations in the linear plant. The use of circular arithmetic is proposed as an accurate but computationally more demanding alternative to the already existing approach based on strict positive realness conditions which is easier and faster to implement but gives, in general, conservative results. Numerical examples are given in order to illustrate the salient features of the mathematical developments. Copyright © 2004 John Wiley & Sons, Ltd.