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Stabilization of linear systems with time‐varying delays
Author(s) -
Wang Guoliang,
Zhang Qingling
Publication year - 2012
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.2845
Subject(s) - control theory (sociology) , interval (graph theory) , stability (learning theory) , basis (linear algebra) , computer science , class (philosophy) , linear matrix inequality , control (management) , mathematics , matrix (chemical analysis) , mathematical optimization , materials science , artificial intelligence , machine learning , composite material , geometry , combinatorics
SUMMARY This paper is concerned with the stability and stabilization problems for a class of time‐delayed systems, whose time‐varying delays are studied via Markovian approach. By separating the delay interval into several subintervals and by considering the inherent distribution of time‐varying delay, a new model is firstly developed. On the basis of the established model, a novel Lyapunov functional, which makes full use of each subinterval's delay bounds and the randomicity of time‐varying delay, is constructed to drive less conservative stability criteria. Especially sufficient conditions for the existence of stabilizing controllers are obtained as linear matrix inequalities, which are further used to deal with networked control systems. Finally, numerical examples are used to demonstrate the effectiveness of the proposed methods. Copyright © 2012 John Wiley & Sons, Ltd.