Soft Computing

, Volume 21, Issue 3, pp 699–720

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


DOI: 10.1007/s00500-016-2051-z

Cite this article as:
Zheng, CD., Xian, Y. & Wang, Z. Soft Comput (2017) 21: 699. doi:10.1007/s00500-016-2051-z


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.


Impulse Fuzzy neural networks Linear convex combination Reciprocal convex technique Third-order reciprocally convex approach 

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.School of ScienceDalian Jiaotong UniversityDalianPeople’s Republic of China
  2. 2.School of Information Science and EngineeringNortheastern UniversityShenyangPeople’s Republic of China

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