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On robust stability of uncertain systems with multiple time‐delays
Author(s) -
Zhou Tong
Publication year - 2010
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.1542
Subject(s) - parametric statistics , mathematics , control theory (sociology) , stability (learning theory) , matrix (chemical analysis) , lti system theory , property (philosophy) , basis (linear algebra) , robust control , linear system , time complexity , computer science , algorithm , control system , mathematical analysis , control (management) , engineering , philosophy , statistics , materials science , geometry , electrical engineering , epistemology , artificial intelligence , machine learning , composite material
On the basis of an infinite to one mapping and the structure of the null space of a multivariate matrix polynomial (MMP), a novel sufficient condition is derived in this paper for the robust stability of a linear time‐invariant system with multiple uncertain time‐delays, parametric modelling errors and unmodelled dynamics. This condition depends on time‐delay bounds and is less conservative than the existing ones. An attractive property is that this condition becomes also necessary in some physically meaningful situations, such as the case that there is only one uncertain time‐delay and neither parametric perturbations nor unmodelling errors exist. Moreover, using ideas of representing a positive‐definite MMP through matrix sum of squares, an asymptotic necessary and sufficient condition is derived for the robust stability of this system. All the conditions can be converted to linear matrix inequalities. Copyright © 2009 John Wiley & Sons, Ltd.