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Robust stability of nonlinear time‐delay systems with interval time‐varying delay
Author(s) -
Orihuela L.,
Millan P.,
Vivas C.,
Rubio F. R.
Publication year - 2011
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.1616
Subject(s) - control theory (sociology) , interval (graph theory) , mathematics , nonlinear system , time derivative , bounded function , stability (learning theory) , upper and lower bounds , norm (philosophy) , computer science , control (management) , mathematical analysis , physics , combinatorics , quantum mechanics , artificial intelligence , machine learning , political science , law
Abstract This paper deals with the problem of obtaining delay‐dependent stability conditions and L 2 ‐gain analysis for a class of nonlinear time‐delay systems with norm‐bounded and possibly time‐varying uncertainties. No restrictions on the derivative of the time‐varying delay are imposed, though lower and upper bounds of the delay interval are assumed to be known. A Lyapunov–Krasovskii functional approach is proposed to derive novel delay‐dependent stability conditions which are expressed in terms of linear matrix inequalities (LMIs). To reduce conservatism, the work exploits the idea of splitting the delay interval in multiple regions, so that specific conditions can be imposed to a unique functional in the different regions. This improves the computed bounds for certain delay‐dependent integral terms, providing less conservative LMI conditions. Examples are provided to demonstrate the reduced conservatism with respect to the available results in the literature. Copyright © 2010 John Wiley & Sons, Ltd.