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New results on delay‐dependent stability analysis and stabilization for stochastic time‐delay systems
Author(s) -
Song Bo,
Park Ju H.,
Wu ZhengGuang,
Li Xuchao
Publication year - 2013
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.3008
Subject(s) - control theory (sociology) , stability (learning theory) , computer science , control (management) , machine learning , artificial intelligence
SUMMARY This paper investigates the problems of stability analysis and stabilization for stochastic time‐delay systems. Firstly, this paper uses the martingale theory to investigate expectations of stochastic cross terms containing the Itô integral. On the basis of this, an improved delay‐dependent stability criterion is derived for stochastic delay systems. In the derivation process, the mathematical development avoids bounding stochastic cross terms, and neither model transformation method nor free‐weighting‐matrix method is used. Thus, the method leads to a simple criterion and shows less conservatism. Secondly, on the basis of this stability result, this paper further proposes a state‐feedback controller that exponentially stabilizes the stochastic delay system by a strict LMI. Therefore, unlike previous results, it is not necessary to transform the nonlinear matrix inequalities into LMIs by the cone complementarity linearization method or parameter‐tuning method, which always yield a suboptimal solution. Finally, examples are provided to demonstrate the reduced conservatism of the proposed conditions.Copyright © 2013 John Wiley & Sons, Ltd.