Skip to main content
Top
Published in: International Journal of Machine Learning and Cybernetics 10/2018

22-04-2017 | Original Article

New results on convergence of fuzzy cellular neural networks with multi-proportional delays

Published in: International Journal of Machine Learning and Cybernetics | Issue 10/2018

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this paper, we propose and study the global exponential convergence of a class of fuzzy cellular neural networks with multi-proportional delays, which has not been studied in the existing literature. Applying the differential inequality technique and Lyapunov functional method, we establish a set of global exponential convergence criteria. The sufficient criteria can be easily tested in practice by simple algebra computations. The obtained results play an important role in designing fuzzy neural networks. Moreover, an illustrative example is given to demonstrate our theoretical results.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Show more products
Literature
1.
go back to reference Chua LO, Roska T (1990) Cellular neural networks with nonlinear and delay-type template elements. In: Proceeding 1990 IEEE Int. Workshop on cellular neural networks and their applications, pp 12–25 Chua LO, Roska T (1990) Cellular neural networks with nonlinear and delay-type template elements. In: Proceeding 1990 IEEE Int. Workshop on cellular neural networks and their applications, pp 12–25
2.
go back to reference Xu Y (2014) New results on almost periodic solutions for CNNs with time-varying leakage delays. Neural Comput Appl 25:1293–1302CrossRef Xu Y (2014) New results on almost periodic solutions for CNNs with time-varying leakage delays. Neural Comput Appl 25:1293–1302CrossRef
3.
go back to reference Zhang A (2015) New results on exponential convergence for cellular neural networks with continuously distributed leakage delays. Neural Process Lett 41:421–433CrossRef Zhang A (2015) New results on exponential convergence for cellular neural networks with continuously distributed leakage delays. Neural Process Lett 41:421–433CrossRef
4.
go back to reference Kwon O, Park J (2009) Exponential stability analysis for uncertain neural networks with interval time-varying delays. Appl Math Comput 212:530–541MathSciNetMATH Kwon O, Park J (2009) Exponential stability analysis for uncertain neural networks with interval time-varying delays. Appl Math Comput 212:530–541MathSciNetMATH
5.
go back to reference Wu J (2001) Introduction to neural dynamics and signal trasmission delay. Walter de Gruyter, BelinCrossRef Wu J (2001) Introduction to neural dynamics and signal trasmission delay. Walter de Gruyter, BelinCrossRef
6.
go back to reference Liu B (2015) Pseudo almost periodic solutions for CNNs with continuously distributed leakage delays. Neural Process Lett 42:233–256CrossRef Liu B (2015) Pseudo almost periodic solutions for CNNs with continuously distributed leakage delays. Neural Process Lett 42:233–256CrossRef
7.
go back to reference Wu X, Wang Y, Huang L, Zuo Y (2010) Robust exponential stability criterion for uncertain neural networks with discontinuous activation functions and time-varying delays. Neurocomputing 73:1265–1271CrossRef Wu X, Wang Y, Huang L, Zuo Y (2010) Robust exponential stability criterion for uncertain neural networks with discontinuous activation functions and time-varying delays. Neurocomputing 73:1265–1271CrossRef
8.
go back to reference Liao X, Chen G, Sanchez EN (2002) LMI-based approach for asymptotically stability analysis of delayed neural networks. IEEE Trans Circuits Syst I Fundam Theory Appl 49(7):1033–1039MathSciNetCrossRefMATH Liao X, Chen G, Sanchez EN (2002) LMI-based approach for asymptotically stability analysis of delayed neural networks. IEEE Trans Circuits Syst I Fundam Theory Appl 49(7):1033–1039MathSciNetCrossRefMATH
9.
go back to reference Xiao J, Zhong S, Li Y (2016) Relaxed dissipativity criteria for memristive neural networks with leakage and time-varying delays. Neurocomputing 171:708–718CrossRef Xiao J, Zhong S, Li Y (2016) Relaxed dissipativity criteria for memristive neural networks with leakage and time-varying delays. Neurocomputing 171:708–718CrossRef
10.
go back to reference Xiao J, Zhong S, Li Y (2015) New passivity criteria for memristive uncertain neural networks with leakage and time-varying delays. ISA T 59:133–148CrossRef Xiao J, Zhong S, Li Y (2015) New passivity criteria for memristive uncertain neural networks with leakage and time-varying delays. ISA T 59:133–148CrossRef
11.
go back to reference Xiao J, Zhong S, Li Y (2016) Improved passivity criteria for memristive neural networks with interval multiple time-varying delays. Neurocomputing 171:1414–1430CrossRef Xiao J, Zhong S, Li Y (2016) Improved passivity criteria for memristive neural networks with interval multiple time-varying delays. Neurocomputing 171:1414–1430CrossRef
12.
go back to reference Yang T, Yang L, Wu C, Chua L (1996) Fuzzy cellular neural networks: theory. In: Proceedings of IEEE International Work shop on cellular neural networks and applications, pp 181–186 Yang T, Yang L, Wu C, Chua L (1996) Fuzzy cellular neural networks: theory. In: Proceedings of IEEE International Work shop on cellular neural networks and applications, pp 181–186
13.
go back to reference Yang T, Yang L, Wu C, Chua L (1996) Fuzzy cellular neural networks: applications. In: Proceedings of IEEE International Work shop on cellular neural networks and applications, pp 225–230 Yang T, Yang L, Wu C, Chua L (1996) Fuzzy cellular neural networks: applications. In: Proceedings of IEEE International Work shop on cellular neural networks and applications, pp 225–230
14.
go back to reference Abdurahman A, Jiang H, Teng Z (2015) Finite-time synchronization for fuzzy cellular neural networks with time-varying delays. Fuzzy Sets Syst 297:96–111MathSciNetCrossRefMATH Abdurahman A, Jiang H, Teng Z (2015) Finite-time synchronization for fuzzy cellular neural networks with time-varying delays. Fuzzy Sets Syst 297:96–111MathSciNetCrossRefMATH
15.
go back to reference Yang HZ, Sheng L (2009) Robust stability of uncertain stochastic fuzzy cellular neural networks. Neurocomputing 73:133–138CrossRef Yang HZ, Sheng L (2009) Robust stability of uncertain stochastic fuzzy cellular neural networks. Neurocomputing 73:133–138CrossRef
16.
go back to reference Jian J, Jiang W (2015) Lagrange exponential stability for fuzzy Cohen–Grossberg neural networks with time-varying delays. Fuzzy Sets Syst 277:65–80MathSciNetCrossRefMATH Jian J, Jiang W (2015) Lagrange exponential stability for fuzzy Cohen–Grossberg neural networks with time-varying delays. Fuzzy Sets Syst 277:65–80MathSciNetCrossRefMATH
17.
go back to reference Zheng C, Zhang X, Wang Z (2015) Mode-dependent stochastic stability criteria of fuzzy Markovian jumping neural networks with mixed delays. ISA Trans 56:8–17CrossRef Zheng C, Zhang X, Wang Z (2015) Mode-dependent stochastic stability criteria of fuzzy Markovian jumping neural networks with mixed delays. ISA Trans 56:8–17CrossRef
18.
go back to reference 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 63:18–30CrossRefMATH 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 63:18–30CrossRefMATH
19.
go back to reference Song X, Zhao P, Xing Z, Peng J (2016) Global asymptotic stability of CNNs with impulses and multi-proportional delays. Math Methods Appl Sci 39:722–733MathSciNetCrossRefMATH Song X, Zhao P, Xing Z, Peng J (2016) Global asymptotic stability of CNNs with impulses and multi-proportional delays. Math Methods Appl Sci 39:722–733MathSciNetCrossRefMATH
20.
go back to reference Dovrolis C, Stiliadisd D, Ramanathan P (1999) Proportional differentiated services: delay differentiation and packet scheduling. ACM Sigcomm Comput Commun Rev 29(4):109–120CrossRef Dovrolis C, Stiliadisd D, Ramanathan P (1999) Proportional differentiated services: delay differentiation and packet scheduling. ACM Sigcomm Comput Commun Rev 29(4):109–120CrossRef
21.
go back to reference Zhang Y, Zhou L (2012) Exponential stability of a class of cellular neural networks with multi-pantograph delays. Acta Electron Sin 40(6):1159–1163 Zhang Y, Zhou L (2012) Exponential stability of a class of cellular neural networks with multi-pantograph delays. Acta Electron Sin 40(6):1159–1163
22.
go back to reference Zhou L (2013) Delay-dependent exponential stability of cellular neural networks with multi-proportional delays. Neural Process Lett 38:347–359CrossRef Zhou L (2013) Delay-dependent exponential stability of cellular neural networks with multi-proportional delays. Neural Process Lett 38:347–359CrossRef
23.
go back to reference Zhou L, Liu J (2013) Global asymptotic stability of a class of cellular neural networks with proportional delays. Chin J Eng Math 5(30):673–682MathSciNetMATH Zhou L, Liu J (2013) Global asymptotic stability of a class of cellular neural networks with proportional delays. Chin J Eng Math 5(30):673–682MathSciNetMATH
24.
go back to reference Zhou L (2015) Novel global exponential stability criteria for hybrid BAM neural networks with proportional delays. Neurocomputing 161:99–106CrossRef Zhou L (2015) Novel global exponential stability criteria for hybrid BAM neural networks with proportional delays. Neurocomputing 161:99–106CrossRef
25.
go back to reference Liu B (2016) Global exponential convergence of non-autonomous cellular neural networks with multi-proportional delays. Neurocomputing 191:352–355CrossRef Liu B (2016) Global exponential convergence of non-autonomous cellular neural networks with multi-proportional delays. Neurocomputing 191:352–355CrossRef
26.
go back to reference Ockendon JR, Tayler AB (1971) The dynamics of a current collection systemfor an electric locomotive. Proc R Soc Lond Ser A Math PhysEng Sci 322:447–468CrossRef Ockendon JR, Tayler AB (1971) The dynamics of a current collection systemfor an electric locomotive. Proc R Soc Lond Ser A Math PhysEng Sci 322:447–468CrossRef
28.
go back to reference Yu Y (2016) Global exponential convergence for a class of neutral functional differential equations with proportional delays. Math Methods Appl Sci 39:4520–4525MathSciNetCrossRefMATH Yu Y (2016) Global exponential convergence for a class of neutral functional differential equations with proportional delays. Math Methods Appl Sci 39:4520–4525MathSciNetCrossRefMATH
30.
go back to reference Derfel GA (1990) Kato problem for functional-differential equations and difference Schr\(\ddot{\rm {o}}\)dinger operators. Oper Theory Adv Appl 46:319–321 Derfel GA (1990) Kato problem for functional-differential equations and difference Schr\(\ddot{\rm {o}}\)dinger operators. Oper Theory Adv Appl 46:319–321
Metadata
Title
New results on convergence of fuzzy cellular neural networks with multi-proportional delays
Publication date
22-04-2017
Published in
International Journal of Machine Learning and Cybernetics / Issue 10/2018
Print ISSN: 1868-8071
Electronic ISSN: 1868-808X
DOI
https://doi.org/10.1007/s13042-017-0672-x

Other articles of this Issue 10/2018

International Journal of Machine Learning and Cybernetics 10/2018 Go to the issue