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Neural Computing and Applications

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19-04-2018 | Original Article

New stability results for impulsive neural networks with time delays

Authors: Chao Liu, Xiaoyang Liu, Hongyu Yang, Guangjian Zhang, Qiong Cao, Junjian Huang

Published in: Neural Computing and Applications | Issue 10/2019

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Abstract

This paper investigates the stability of impulsive neural networks with time delays. Based on a new tool called as uniformly exponentially convergent functions, an improved Razumikhin method leads to new, more permissive stability results. By comparison with the existing results, the rigorous restrictions on impulses, which are presented in the previous Razumikhin stability theorems, are removed. Moreover, the obtained results do not restrict that the time derivative of Lyapunov function is negative definite or positive definite under the Razumikhin condition. The effectiveness of the proposed results is demonstrated by three simple numerical examples.

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Leung CS, Chan LW, Lai E (1995) Stability, capacity, and statistical dynamics of second-order bidirectional associative memory. IEEE Trans Syst Man Cybern 25(10):1414–1424

Juang JC (1999) Stability analysis of Hopfield-type neural networks. IEEE Trans Neural Netw 10(6):1366–1374

Yang H, Dillon TS (1994) Exponential stability and oscillation of Hopfield graded response neural network. IEEE Trans Neural Netw 5(5):719–729

Lee DL (1999) New stability conditions for Hopfield networks in partial simultaneous update mode. IEEE Trans Neural Netw 10(4):975–978MathSciNet

Chen WH, Zheng WX (2010) A new method for complete stability analysis of cellular neural networks with time delay. IEEE Trans Neural Netw 21(7):1126–1239

Arik S (2003) Global asymptotic stability of a larger class of neural networks with constant time delay. Phys Lett A 311(6):504–511MATH

Arik S, Tavsanoglu V (2005) Global asymptotic stability analysis of bidirectional associative memory neural networks with constant time delays. IEEE Trans Neural Netw 68(3):161–176

Chen WH, Zheng WX (2009) Global exponential stability of impulsive neural networks with variable delay: an LMI approach. IEEE Trans Circuits Syst I 56(6):1248–1259MathSciNet

Shao H (2008) Delay-dependent stability for recurrent neural networks with time-varying delays. IEEE Trans Neural Netw 19(9):1647–1651

10.

Aouiti C, MHamdi MS, Touati A (2017) Pseudo almost automorphic solutions of recurrent neural networks with time-varying coefficients and mixed delays. Neural Process Lett 45:121–140

11.

Liu Y, Wang Z, Liu X (2006) Global exponential stability of generalized recurrent neural networks with discrete and distributed delays. Neural Netw 19(5):667–675MATH

12.

Li T, Song A, Fei S, Wang T (2010) Delay-derivative-dependent stability for delayed neural networks with unbound distributed delay. IEEE Trans Neural Netw 21(8):1365–1371

13.

Luo WW, Zhong K, Zhu S, Shen Y (2014) Further results on robustness analysis of global exponential stability of recurrent neural networks with time delays and random disturbances. Neural Netw 53:127–133MATH

14.

Li CD, Liao XF (2006) Robust stability and robust periodicity of delayed recurrent neural networks with noise disturbance. IEEE Trans Circuits Syst I Regul Pap 53(10):2265–2273

15.

Faydasicok O, Arik S (2012) Equilibrium and stability analysis of delayed neural networks under parameter uncertainties. Appl Math Comput 218(12):6716–6726MathSciNetMATH

16.

Arik S (2014) New criteria for global robust stability of delayed neural networks with norm-bounded uncertainties. IEEE Trans Neural Netw Learn Syst 25(6):1045–1052MathSciNet

17.

Samidurai R, Anthoni SM, Balachandran K (2010) Global exponential stability of neutral-type impulsive neural networks with discrete and distributed delays. Nonlinear Anal Hybrid Syst 4(1):103–112MathSciNetMATH

18.

Gao Y, Zhou WN, Ji C, Tong DB, Fang JA (2012) Globally exponential stability of stochastic neutral-type delayed neural networks with impulsive perturbations and Markovian switching. Nonlinear Dyn 70(3):2107–2116MathSciNetMATH

19.

Zhu QX, Cao JD (2010) Robust exponential stability of markovian jump impulsive stochastic Cohen–Grossberg neural networks with mixed time delays. IEEE Trans Neural Netw 21(8):1314–1325

20.

Wang Y, Zheng CD, Feng EM (2013) Stability analysis of mixed recurrent neural networks with time delay in the leakage term under impulsive perturbations. Neurocomputing 119(16):454–461

21.

Zhu QX, Rakkiyappan R, Chandrasekar A (2014) Stochastic stability of Markovian jump BAM neural networks with leakage delays and impulse control. Neurocomputing 136(1):136–151

22.

Aouiti C (2016) Neutral impulsive shunting inhibitory cellular neural networks with time-varying coefficients and leakage delays. Cogn Neurodyn 10(6):573–591MathSciNet

23.

Aouiti C (2016) Oscillation of impulsive neutral delay generalized high-order Hopfield neural networks. Neural Comput Appl. https://doi.org/10.1007/s00521-016-2558-3 CrossRef

24.

Aouiti C, MHamdi MS, Cao J, Alsaedi A (2017) Piecewise pseudo almost periodic solution for impulsive generalised high-order Hopfield neural networks with leakage delays. Neural Process Lett 45(2):615–648

25.

Li CD, Feng G, Huang TW (2008) On hybrid impulsive and switching neural networks. IEEE Trans Syst Man Cybern B 38(6):1549–1560

26.

Fu XL, Li XD (2009) Global exponential stability and global attractivity of impulsive Hopfield neural networks with time delays. J Comput Appl Math 231(1):187–199MathSciNetMATH

27.

Liu C, Li CD, Liao XF (2011) Variable-time impulses in BAM neural networks with delays. Neurocomputing 74(17):3286–3295

28.

Hale JK (1977) Theory of functional differential equations. Springer, New YorkMATH

29.

Wu QJ, Zhou J, Xiang L (2010) Global exponential stability of impulsive differential equations with any time delays. Appl Math Lett 23(2):143–147MathSciNetMATH

30.

Wang Q, Liu XZ (2007) Impulsive stabilization of delay differential systems via the Lyapunov–Razumikhin method. Appl Math Lett 20(8):839–845MathSciNetMATH

31.

Lin DW, Li XD, ORegan D (2012) Stability analysis of generalized impulsive functional differential equations. Math Comput Model 55(5–6):1682–1690MathSciNetMATH

32.

Wang HM, Duan SK, Li CD, Wang LD, Huang TW (2016) Globally exponential stability of delayed impulsive functional differential systems with impulse time windows. Nonlinear Dyn 84(3):1655–1665MathSciNetMATH

33.

Zhu QX (2014) \(p\)th Moment exponential stability of impulsive stochastic functional differential equations with Markovian switching. J Franklin Inst 351(7):3965–3986MathSciNetMATH

34.

Cheng P, Deng FQ, Yao FQ (2014) Exponential stability analysis of impulsive stochastic functional differential systems with delayed impulses. Commun Nonlinear Sci Numer Simul 19(6):2104–2114MathSciNet

35.

Li XD (2012) Further analysis on uniform stability of impulsive infinite delay differential equations. Appl Math Lett 25(2):133–137MathSciNetMATH

36.

Liu J, Liu XZ, Xie WC (2011) Impulsive stabilization of stochastic functional differential equations. Appl Math Lett 24(3):264–269MathSciNetMATH

37.

Li XD (2010) New results on global exponential stabilization of impulsive functional differential equations with infinite delays or finite delays. Commun Nonlinear Sci Numer Simul 11(5):4194–4201MathSciNetMATH

38.

Li XD, Fu XL (2014) On the global exponential stability of impulsive functional differential equations with infinite delays or finite delays. Commun Nonlinear Sci Numer Simul 19(3):442–447MathSciNet

39.

Xing YP, Han MA (2004) A new approach to stability of impulsive functional differential equations. Appl Math Comput 151(3):835–847MathSciNetMATH

40.

Wang Q, Liu XZ (2005) Exponential stability for impulsive delay differential equations by Razumikhin method. J Math Anal Appl 309(2):462–473MathSciNetMATH

41.

Chen Z, Fu XL (2007) New Razumikhin-type theorems on the stability for impulsive functional differential systems. Nonlinear Anal 66(9):2040–2052MathSciNetMATH

42.

Liu B, Liu XZ, Teo KL, Wang Q (2006) Razumikhin-type theorems on exponential stability of impulsive delay systems. IMA J Appl Math 71(1):47–61MathSciNetMATH

43.

Li XD, Fu XL (2009) Razumikhin-type theorems on exponential stability of impulsive infinite delay differential systems. J Comput Appl Math 224(1):1–10MathSciNetMATH

44.

Luo ZG, Shen JH (2009) Stability of impulsive functional differential equations via the Liapunov functional. Appl Math Lett 22(2):163–169MathSciNet

45.

Luo ZG, Shen JH (2001) Stability results for impulsive functional differential equations with infinite delays. J Comput Appl Math 131(1–2):55–64MathSciNetMATH

46.

Zhang Y, Sun JT (2005) Strict stability of impulsive functional differential equations. J Math Anal Appl 301(1):237–248MathSciNetMATH

47.

Li XD, Song SJ (2013) Impulsive control for existence, uniqueness, and global stability of periodic solutions of recurrent neural networks with discrete and continuously distributed delays. IEEE Trans Neural Netw Learn Syst 24(6):868–877

48.

Duan SK, Wang HM, Wang LD, Huang TW, Li CD (2017) Impulsive effects and stability analysis on memristive neural networks with variable delays. IEEE Trans Neural Netw Learn Syst 28(2):476–481

49.

Wu B, Liu Y, Lu JQ (2012) New results on global exponential stability for impulsive cellular neural networks with any bounded time-varying delays. Math Comput Model 55(3–4):837–843MathSciNetMATH

50.

Li CD, Shen YY, Feng G (2009) Stabilizing effects of impulses in delayed BAM neural networks. IEEE Trans Circuits Syst II Express Briefs 55(12):1284–1288

51.

Wu SC, Li CD, Liao XF, Duan SK (2012) Exponential stability of impulsive discrete systems with time delay and applications in stochastic neural networks: a Razumikhin approach. Neurocomputing 84(4):29–36

52.

Mazenc F, Malisoff M (2015) Trajectory based approach for the stability analysis of nonlinear systems with time delays. IEEE Trans Autom Control 60(6):1716–1721MathSciNetMATH

Title: New stability results for impulsive neural networks with time delays
Authors: Chao Liu
Xiaoyang Liu
Hongyu Yang
Guangjian Zhang
Qiong Cao
Junjian Huang
Publication date: 19-04-2018
Publisher: Springer London
Published in: Neural Computing and Applications / Issue 10/2019
Print ISSN: 0941-0643
Electronic ISSN: 1433-3058
DOI: https://doi.org/10.1007/s00521-018-3481-6

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