Third-order reciprocally convex approach to stability of fuzzy cellular neural networks under impulsive perturbations

The stability is investigated for a kind of fuzzy cellular neural networks with time-varying and continuously distributed delays under impulsive perturbations. When the Wirtinger-based integral inequality is applied to partitioned integral terms in the derivation of matrix inequality conditions, a n...

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Bibliographic Details
Published inSoft computing (Berlin, Germany) Vol. 21; no. 3; pp. 699 - 720
Main Authors Zheng, Cheng-De, Xian, Yongjin, Wang, Zhanshan
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2017
Springer Nature B.V
Subjects
Artificial Intelligence
Artificial neural networks
Cellular communication
Computational Intelligence
Control
Engineering
Equilibrium
Foundations
Fuzzy logic
Inequality
Investigations
Lower bounds
Mathematical analysis
Mathematical Logic and Foundations
Mechatronics
Neural networks
Perturbation
Robotics
Stability
Third-order reciprocally convex approach
Fuzzy neural networks
Reciprocal convex technique
Linear convex combination
Impulse
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Summary:The stability is investigated for a kind of fuzzy cellular neural networks with time-varying and continuously distributed delays under impulsive perturbations. When the Wirtinger-based integral inequality is applied to partitioned integral terms in the derivation of matrix inequality conditions, a new kind of linear combination of positive functions emerges weighted by the inverses of cubic convex parameters. This paper proposes an efficient method called third-order reciprocally convex approach to manipulate such a combination by extending the reciprocal convex technique. By utilizing Briat lemma and reciprocal convex approach, this paper derives several novel sufficient conditions to ensure the global asymptotic stability of the equilibrium point of the considered networks. Based on the derived criteria, a lower-bound estimation can be obtained of the largest stability interval for a class of fuzzy cellular neural networks under impulsive perturbations. Simulation examples demonstrate that the presented method can significantly reduce the conservatism of the existing results, and lead to wider applications.
ISSN:1432-7643
1433-7479
DOI:10.1007/s00500-016-2051-z