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Neural Computing and Applications

Erschienen in:

01.02.2015 | Original Article

Stochastic stability analysis for neural networks with mixed time-varying delays

verfasst von: Yuechao Ma, Yuqing Zheng

Erschienen in: Neural Computing and Applications | Ausgabe 2/2015

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Abstract

This paper is concerned with the problem of the stochastic stability analysis for Markovian jumping neural networks with time-varying delays and stochastic perturbation. Some criteria for the stability and robust stability of such neural networks are derived, by means of constructing suitable Lyapunov–Krasovskii functionals and a unified linear matrix inequality (LMI) approach. Note that the LMIs can be easily solved by using the Matlab LMI toolbox and no tuning of parameters is required. Finally, numerical examples are used to illustrate the effectiveness and advantage of the proposed techniques.

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Xu S, Lam J, Dwc Ho (2005) Novel global asymptotical stability criteria for delayed cellular neural networks. IEEE Trans Circuits Syst 52:349–353CrossRef

Chen A, Cao J, Huang L (2005) Global robust stability of interval cellular neural networks with time varying delays. Chaos Solitons Fractals 23(3):789–799CrossRefMathSciNet

Zhang Q, Wei X, Xu J (2006) Stability analysis for cellular neural networks with variable delays. Chaos Solitons Fractals 28(2):331–336CrossRefMATHMathSciNet

Hong L, Bing C (2008) Robust exponential stability for delayed uncertain Hopfield neural networks with Markovian jumping parameters. Phys Lett A 372:4996–5003CrossRefMathSciNet

Mao X (2002) Exponential stability of stochastic delay interval systems with Markovian switching. IEEE Trans Autom Control 47:1604–1612CrossRef

Zhang J, Jin X (2000) Global stability analysis in delayed Hopfield neural network models. Neural Netw 13:745–753CrossRef

Cao J, Wang J (2003) Global asymptotic stability of reaction diffusion recurrent neural networks with time-varying delays. Phys Lett A 314:434–442CrossRefMATH

Syed Ali M, Balasubramaniam P (2008) Robust stability for uncertain stochastic fuzzy BAM neural networks with time-varying delays. Phys Lett A 372(31):5159–5166CrossRefMATHMathSciNet

Balasubramaniam P, Lakshmanan S, Rakkiyappan R (2009) Delay-interval dependent robust stability criteria for stochastic neural networks with linear fractional uncertainties. Neurocomputing 72(16):3675–3682CrossRef

10.

Rakkiyappan R, Balasubramaniam P (2008) Delay-dependent asymptotic stability for stochastic delayed recurrent neural networks with time varying delays. Appl Math Comput 198(2):526–533CrossRefMATHMathSciNet

11.

Cao J, Wang J (2005) Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Trans Circuits Syst 23(1):221–229MATH

12.

Zhang H, Liu Z, Wang Z (2010) Novel weighting delay-based stability criteria for recurrent neural networks with time-varying delays. IEEE Trans Neural Netw 21:91–106CrossRef

13.

Huang C, Cao J (2009) Almost sure exponential stability of stochastic cellular neural networks with unbounded distributed delays. Neurocomputing 72(13–15):3352–3356CrossRef

14.

Rakkiyappan R, Balasubramaniam P (2008) LMI conditions for global asymptotic stability results for neutral-type neural networks with distributed time delays. Appl Math Comput 204(1):317–324CrossRefMATHMathSciNet

15.

Shi P, Zhang J, Qiu J, Xing L (2006) New global asymptotic stability criterion for neural networks with discrete and distributed delays. Proc Inst Mech Eng J Syst Control Eng 221:129–135

16.

Balasubramaniam P, Rakkiyappan R (2008) Global asymptotic stability of stochastic recurrent neural networks with multiple discrete delays and unbounded distributed delays. Appl Math Comput 204(2):680–686CrossRefMATHMathSciNet

17.

Cao J, Wang J (2003) Global asymptotic stability of a general class of recurrent neural networks with time-varying delays. IEEE Trans Circuits Syst 50(1):34–44CrossRefMathSciNet

18.

Liu Y, Wang Z, Liu X (2008) On delay-dependent robust exponential stability of stochastic neural networks with mixed time delays and Markovian switching. Nonlinear Dyn 54:199–212CrossRefMATH

19.

Gao H, Shi P, Wang J (2007) Parameter-dependent robust stability of uncertain time-delay systems. J Comput Appl Math 206(1):366–373CrossRefMATHMathSciNet

20.

Han Q (2004) On robust stability of neutral systems with time-varying discrete delay and norm-bounded uncertainty. Automatica 40(6):1087–1092CrossRefMATHMathSciNet

21.

Mahmoud MS, Shi P, Nounou HN (2007) Resilient observer-based control of uncertain time-delay system. Int J Innov Comput Inf Control 3(2):407–418

22.

Han Q (2005) On stability of linear neutral systems with mixed time delays: a discretized Lyapunov functional approach. Automatica 41:1209–1218CrossRefMATH

23.

Liu B (2013) Global exponential stability for BAM neural networks with time-varying delays in the leakage terms. Nonlinear Anal Real World Appl 14:559–566CrossRefMATHMathSciNet

24.

Faydasicok O, Arik S (2012) Robust stability analysis of a class of neural networks with discrete time delays. Neural Netw 29:52–59CrossRef

25.

Liu H, Zhao L, Zhang Z (2009) Stochastic stability of Markovian jumping neural networks with constant and distribute delays. Neurocomputing 72:3669–3674CrossRef

26.

Huang H, Ho DWC, Qu Y (2007) Robust stability of stochastic delayed additive neural networks with Markovian switching. Neural Netw 20:799–809CrossRefMATH

27.

Ji Y, Chizeck HJ (1990) Controllability, stability, and continuous-time Markovian jump linear quadratic control. IEEE Trans Autom Control 35:777–788CrossRefMATHMathSciNet

28.

Lou X, Cui B (2007) Delay-dependent stochastic stability of delayed Hopfield neural networks with Markovian jump parameters. J Math Anal Appl 328:316–326CrossRefMATHMathSciNet

29.

Boukas EK, Yang H (1999) Exponential stability of stochastic systems with Markovian jumping parameters. Automatica 35(8):1437–1441CrossRefMATHMathSciNet

30.

Yuan C, Mao X (2004) Robust stability and controllability of stochastic differential delay equations with Markovian switching. Automatica 40(3):343–354CrossRefMATHMathSciNet

31.

Wang G, Cao J, Liang J (2009) Exponential stability in the mean square for stochastic neural networks with mixed time-delays and Markovian jumping parameters. Nonlinear Dyn 57:209–218CrossRefMATHMathSciNet

32.

Wang Z, Liu Y, Yu L, Liu X (2006) Exponential stability of delayed recurrent neural networks with Markovian jumping parameters. Phys Lett A 356:346–352CrossRefMATH

33.

Lou X, Cui B (2009) Stochastic stability analysis for delayed neural networks of neutral type with Markovian jump parameters. Chaos Solitons Fractals 39(5):2188–2197CrossRefMATHMathSciNet

34.

Zhang J, Shi P, Qiu J, Yang H (2008) A new criterion for exponential stability of uncertain stochastic neural networks with mixed delays. Math Comput Model 47(9–10):1042–1051CrossRefMATHMathSciNet

35.

Boyd S, Ghaoui L, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM, PhiladelphiaCrossRefMATH

36.

Skorohod AV (1989) Asymptotic methods in the theory of stochastic differential equations. American Mathematical Society, Providence

Titel: Stochastic stability analysis for neural networks with mixed time-varying delays
verfasst von: Yuechao Ma
Yuqing Zheng
Publikationsdatum: 01.02.2015
Verlag: Springer London
Erschienen in: Neural Computing and Applications / Ausgabe 2/2015
Print ISSN: 0941-0643
Elektronische ISSN: 1433-3058
DOI: https://doi.org/10.1007/s00521-014-1735-5

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