Soft Computing

, Volume 21, Issue 3, pp 699–720 | Cite as

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

Foundations

Abstract

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.

Keywords

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

References

  1. Briat C (2008) Robust control and observation of LPV time-delay systems. Ph.D. thesis, Grenoble INP, FranceGoogle Scholar
  2. Gu K (2000) An integral inequality in the stability problem of time-delay systems. In: Proc. 39th IEEE conf. decision and control, Sydney, pp 2805–2810Google Scholar
  3. Han W, Liu Y, Wang L (2012) Global exponential stability of delayed fuzzy cellular neural networks with Markovian jumping parameters. Neural Comput Appl 21:67–72CrossRefGoogle Scholar
  4. Ji M-D, He Y, Zhang C-K, Wu M (2014) Novel stability criteria for recurrent neural networks with time-varying delay. Neurocomputing 138:383–391CrossRefGoogle Scholar
  5. Kao Y, Shi L, Xie J, Karimi HR (2015) Global exponential stability of delayed Markovian jump fuzzy cellular neural networks with generally incomplete transition probability. Neural Netw 63:18–30CrossRefMATHGoogle Scholar
  6. Lee WI, Park PG (2014) Second-order reciprocally convex approach to stability of systems with interval time-varying delays. Appl Math Comput 229:245–253MathSciNetGoogle Scholar
  7. Li C, Li Y, Ye Y (2010) Exponential stability of fuzzy Cohen–Grossberg neural networks with time delays and impulsive effects. Commun Nonlinear Sci Numer Simul 15:3599–3606MathSciNetCrossRefMATHGoogle Scholar
  8. Li X, Rakkiyappan R, Balasubramaniam P (2011) Existence and global stability analysis of equilibrium of fuzzy cellular neural networks with time delay in the leakage term under impulsive perturbations. J Frankl Inst 348:135–155MathSciNetCrossRefMATHGoogle Scholar
  9. Liu J, Zhang J (2012) Note on stability of discrete-time time-varying delay systems. IET Control Theory Appl 6(2):335–339MathSciNetCrossRefGoogle Scholar
  10. Liu Z, Zhang H, Wang Z (2009) Novel stability criterions of a new fuzzy cellular neural networks with time-varying delays. Neurocomputing 72:1056–1064CrossRefGoogle Scholar
  11. Liu Y, Hu L-S, Shi P (2012) A novel approach on stabilization for linear systems with time-varying input delay. Appl Math Comput 218:5937–5947MathSciNetMATHGoogle Scholar
  12. Park P, Ko JW, Jeong C (2011) Reciprocally convex approach to stability of systems with time-varying delays. Automatica 47(1):235–238MathSciNetCrossRefMATHGoogle Scholar
  13. Seuret A, Gouaisbaut F (2013) Wirtinger-based integral inequality: application to time-delay systems. Automatica 49:2860–2866MathSciNetCrossRefGoogle Scholar
  14. Song Q, Cao J (2007) Impulsive effects on stability of fuzzy Cohen–Grossberg neural networks with time-varying delays. IEEE Trans Syst Man Cyber B Cyber 37(3):733–741Google Scholar
  15. Sun J, Chen J (2013) Stability analysis of static recurrent neural networks with interval time-varying delay. Appl Math Comput 221:111–120Google Scholar
  16. Wei L, Chen W-H (2015) Global exponential stability of a class of impulsive neural networks with unstable continuous and discrete dynamics. Neurocomputing 147:225–234CrossRefGoogle Scholar
  17. Wu Z-G, Shi P, Su H, Chu J (2012) Exponential synchronization of neural networks with discrete and distributed delays under time-varying sampling. IEEE Trans Neural Netw Learn Syst 23(9):1368–1376CrossRefGoogle Scholar
  18. Xing X, Yao D, Lu Q, Li X (2015) Finite-time stability of Markovian jump neural networks with partly unknown transition probabilities. Neurocomputing 159:282–287CrossRefGoogle Scholar
  19. Xie J, Kao Y (2015) Stability of Markovian jump neural networks with mode-dependent delays and generally incomplete transition probability. Neural Comput Appl 26(7):1537–1553CrossRefGoogle Scholar
  20. Yang T, Yang L (1996) The global stability of fuzzy cellular neural networks. IEEE Trans Circuits Syst 43(10):880–883MathSciNetCrossRefGoogle Scholar
  21. Yu S, Zhang Z, Quan Z (2015) New global exponential stability conditions for inertial Cohen–Grossberg neural networks with time delays. Neurocomputing 151(3):1446–1454CrossRefGoogle Scholar
  22. Zhang H, Wang Y (2008) Stability analysis of markovian jumping stochastic Cohen–Grossberg neural networks with mixed time delays. IEEE Trans Neural Netw 19(2):366–370MathSciNetCrossRefGoogle Scholar
  23. Zhang Q, Shao Y, Liu J (2013) Analysis of stability for impulsive fuzzy Cohen–Grossberg BAM neural networks with delays. Math Methods Appl Sci 36(7):773–779Google Scholar
  24. Zhou C, Zhang H, Zhang H, Dang C (2012) Global exponential stability of impulsive fuzzy Cohen–Grossberg neural networks with mixed delays and reaction-diffusion terms. Neurocomputing 91:67–76CrossRefGoogle Scholar

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

Personalised recommendations