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Novel stability criteria for fuzzy Hopfield neural networks based on an improved homogeneous matrix polynomials technique
Alternative TitleNovel stability criteria for fuzzy Hopfield neural networks based on an improved homogeneous matrix polynomials technique
Feng YiFu1; Zhang QingLing2; Feng DeZhi2
2012
Source PublicationCHINESE PHYSICS B
ISSN1674-1056
Volume21Issue:10
AbstractThe global stability problem of Takagi-Sugeno (T-S) fuzzy Hopfield neural networks (FHNNs) with time delays is investigated. Novel LMI-based stability criteria are obtained by using Lyapunov functional theory to guarantee the asymptotic stability of the FHNNs with less conservatism. Firstly, using both Finsler's lemma and an improved homogeneous matrix polynomial technique, and applying an affine parameter-dependent Lyapunov-Krasovskii functional, we obtain the convergent LMI-based stability criteria. Algebraic properties of the fuzzy membership functions in the unit simplex are considered in the process of stability analysis via the homogeneous matrix polynomials technique. Secondly, to further reduce the conservatism, a new right-hand-side slack variables introducing technique is also proposed in terms of LMIs, which is suitable to the homogeneous matrix polynomials setting. Finally, two illustrative examples are given to show the efficiency of the proposed approaches.
Other AbstractThe global stability problem of Takagi-Sugeno (T-S) fuzzy Hopfield neural networks (FHNNs) with time delays is investigated. Novel LMI-based stability criteria are obtained by using Lyapunov functional theory to guarantee the asymptotic stability of the FHNNs with less conservatism. Firstly, using both Finsler's lemma and an improved homogeneous matrix polynomial technique, and applying an affine parameter-dependent Lyapunov-Krasovskii functional, we obtain the convergent LMI-based stability criteria. Algebraic properties of the fuzzy membership functions in the unit simplex are considered in the process of stability analysis via the homogeneous matrix polynomials technique. Secondly, to further reduce the conservatism, a new right-hand-side slack variables introducing technique is also proposed in terms of LMIs, which is suitable to the homogeneous matrix polynomials setting. Finally, two illustrative examples are given to show the efficiency of the proposed approaches.
KeywordTIME-VARYING DELAYS EXPONENTIAL STABILITY STOCHASTIC STABILITY SYSTEMS Hopfield neural networks linear matrix inequality Takagi-Sugeno fuzzy model homogeneous polynomially technique
Indexed ByCSCD
Language英语
Funding Project[National Natural Science Foundation of China] ; [Natural Science Foundation of Jilin Province, China]
CSCD IDCSCD:4701580
Citation statistics
Cited Times:1[CSCD]   [CSCD Record]
Document Type期刊论文
Identifierhttp://ir.imr.ac.cn/handle/321006/149934
Collection中国科学院金属研究所
Affiliation1.吉林师范大学
2.中国科学院金属研究所
Recommended Citation
GB/T 7714
Feng YiFu,Zhang QingLing,Feng DeZhi. Novel stability criteria for fuzzy Hopfield neural networks based on an improved homogeneous matrix polynomials technique[J]. CHINESE PHYSICS B,2012,21(10).
APA Feng YiFu,Zhang QingLing,&Feng DeZhi.(2012).Novel stability criteria for fuzzy Hopfield neural networks based on an improved homogeneous matrix polynomials technique.CHINESE PHYSICS B,21(10).
MLA Feng YiFu,et al."Novel stability criteria for fuzzy Hopfield neural networks based on an improved homogeneous matrix polynomials technique".CHINESE PHYSICS B 21.10(2012).
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