LMI-Based Stability Criterion of Impulsive T-S Fuzzy Dynamic Equations via Fixed Point Theory

By formulating a contraction mapping and the matrix exponential function, the authors apply linear matrix inequality (LMI) technique to investigate and obtain the LMI-based stability criterion of a class of time-delay Takagi-Sugeno (T-S) fuzzy differential equations. To the best of our knowledge, it...

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Published inAbstract and Applied Analysis Vol. 2013; no. 2013; pp. 409 - 417-242
Main Authors Rao, Ruofeng, Pu, Zhilin
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Limiteds 01.01.2013
Hindawi Puplishing Corporation
Hindawi Publishing Corporation
John Wiley & Sons, Inc
Hindawi Limited
Subjects
Criteria
Dynamical systems
Exponential functions
Fixed point theory
Fixed points (mathematics)
Fuzzy
Fuzzy algorithms
Fuzzy logic
Fuzzy set theory
Fuzzy systems
Inequalities (Mathematics)
Mathematical analysis
Mathematical research
Matlab
Stability
Iran
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Summary:By formulating a contraction mapping and the matrix exponential function, the authors apply linear matrix inequality (LMI) technique to investigate and obtain the LMI-based stability criterion of a class of time-delay Takagi-Sugeno (T-S) fuzzy differential equations. To the best of our knowledge, it is the first time to obtain the LMI-based stability criterion derived by a fixed point theory. It is worth mentioning that LMI methods have high efficiency and other advantages in largescale engineering calculations. And the feasibility of LMI-based stability criterion can efficiently be computed and confirmed by computer Matlab LMI toolbox. At the end of this paper, a numerical example is presented to illustrate the effectiveness of the proposed methods.
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ISSN:1085-3375
1687-0409
DOI:10.1155/2013/261353