Robustness analysis of global exponential stability in neural networks evoked by deviating argument and stochastic disturbance

Volume 10, Issue 11, pp 5646--5667 http://dx.doi.org/10.22436/jnsa.010.11.04

Publication Date: November 10, 2017 Submission Date: August 04, 2016

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 2611 Downloads
• 5368 Views

Authors

Liguang Wan - College of Mechatronics and Control Engineering, Hubei Normal University, Huangshi 435002, China. Ailong Wu - College of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China. Jingru Chen - Department of Personnel, Hubei Normal University, Huangshi 435002, China.

Abstract

This paper studies the robustness of global exponential stability of neural networks evoked by deviating argument and stochastic disturbance. Given the original neural network is globally exponentially stable, we discuss the problem that the neural network is still globally exponentially stable when the deviating argument or both the deviating argument and stochastic disturbance is/are generated. By virtue of solving the derived transcendental equation(s), the upper bound(s) about the intensity of the deviating argument or both of the deviating argument and stochastic disturbance is/are received. The obtained theoretical results are the supplements to the existing literatures on global exponential stability of neural networks. Two numerical examples are offered to demonstrate the effectiveness of theoretical results.

Share and Cite

Keywords

• Global exponential stability
• robustness
• neural networks
• deviating argument
• stochastic disturbance

MSC

•  34D23
•  93D09

References

• [1] M. U. Akhmet, D. Aruğaslan, E. Yılmaz, Stability analysis of recurrent neural networks with piecewise constant argument of generalized type, Neural Netw., 23 (2010), 805–811.
  • View Article
  • Google Scholar


• [2] M. U. Akhmet, E. Yılmaz, Impulsive Hopfield-type neural network system with piecewise constant argument, Nonlinear Anal. Real World Appl., 11 (2010), 2584–2593.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [3] G. Bao, S. P. Wen, Z. G. Zeng , Robust stability analysis of interval fuzzy Cohen-Grossberg neural networks with piecewise constant argument of generalized type, Neural Netw., 33 (2012), 32–41.
  • View Article
  • Google Scholar
  • MATH


• [4] J. D. Cao, J. Wang, Global asymptotic stability of a general class of recurrent neural networks with time-varying delays, IEEE Trans. Circuits Systems I Fund. Theory Appl., 50 (2003), 34–44.
  • View Article
  • MathSciNet
  • Google Scholar


• [5] W.-H. Chen, X. M. Lu, Mean square exponential stability of uncertain stochastic delayed neural networks, Phys. Lett. A, 372 (2008), 1061–1069.
  • View Article
  • MathSciNet
  • Google Scholar


• [6] W.-H. Chen, X. M. Lu, W. X. Zheng, Impulsive stabilization and impulsive synchronization of discrete-time delayed neural networks, IEEE Trans. Neural Netw. Learn. Syst., 26 (2015), 734–748.
  • View Article
  • MathSciNet
  • Google Scholar


• [7] W.-H. Chen, S. X. Luo, X. M. Lu, Multistability in a class of stochastic delayed Hopfield neural networks, Neural Netw., 68 (2015), 52–61.
  • View Article
  • Google Scholar


• [8] J. J. Chen, Z. G. Zeng, P. Jiang, Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks, Neural Netw., 51 (2014), 1–8.
  • View Article
  • Google Scholar
  • MATH


• [9] W.-H. Chen, W. X. Zheng, A new method for complete stability analysis of cellular neural networks with time delay, IEEE Trans. Neural Netw., 21 (2010), 1126–1139.
  • View Article
  • Google Scholar


• [10] Y. Chen,W. X. Zheng, Stochastic state estimation for neural networks with distributed delays and Markovian jump, Neural Netw., 25 (2012), 14–20.
  • View Article
  • Google Scholar
  • MATH


• [11] F. Q. Deng, M. G. Hua, X. Z. Liu, Y. J. Peng, J. T. Fei , Robust delay-dependent exponential stability for uncertain stochastic neural networks with mixed delays, Neurocomputing, 74 (2011), 1503–1509.
  • View Article
  • Google Scholar


• [12] S. B. Ding, Z. S. Wang, Stochastic exponential synchronization control of memristive neural networks with multiple timevarying delays, Neurocomputing, 162 (2015), 16–25.
  • View Article
  • Google Scholar


• [13] Z. Y. Guo, J. Wang, Z. Yan, Global exponential dissipativity and stabilization of memristor-based recurrent neural networks with time-varying delays, Neural Netw., 48 (2013), 158–172.
  • View Article
  • Google Scholar
  • MATH


• [14] Z. Y. Guo, J. Wang, Z. Yan, Global exponential synchronization of two memristor-based recurrent neural networks with time delays via static or dynamic coupling, IEEE Trans. Syst., Man, Cybern., Syst., 45 (2015), 235–249.
  • View Article
  • Google Scholar


• [15] G. Huang, J. D. Cao, Multistability in bidirectional associative memory neural networks, Phys. Lett. A, 372 (2008), 2842–2854.
  • View Article
  • Google Scholar
  • MATH


• [16] P. Li, J. D. Cao, Z. D. Wang , Robust impulsive synchronization of coupled delayed neural networks with uncertainties, Phys. A, 373 (2007), 261–272.
  • View Article
  • Google Scholar


• [17] H. Y. Li, K. C. Cheung, J. Lam, H. J. Gao , Robust stability for interval stochastic neural networks with time-varying discrete and distributed delays, Differ. Equ. Dyn. Syst., 19 (2011), 97–118.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [18] J. L. Liang, Z. D. Wang, Y. R. Liu, X. H. Liu, Global synchronization control of general delayed discrete-time networks with stochastic coupling and disturbances, IEEE Trans. Syst., Man, Cybern., Syst., 38 (2008), 1073–1083.
  • View Article
  • Google Scholar


• [19] D. R. Liu, S. Q. Hu, J. Wang, Global output convergence of a class of continuous-time recurrent neural networks with time-varying thresholds, IEEE Trans. Circuits Syst. II Expr. Bri., 51 (2004), 161–167.
  • View Article
  • Google Scholar


• [20] L. Liu, A. L.Wu, X. G. Song, Global \(O(t^{-\alpha})\) stabilization of fractional-order memristive neural networks with time delays, SpringerPlus, 5 (2016), 22 pages.


• [21] L. Liu, A. L. Wu, Z. G. Zeng, T. W. Huang , Global mean square exponential stability of stochastic neural networks with retarded and advanced argument, Neurocomputing, 247 (2017), 156–164.
  • View Article
  • Google Scholar


• [22] P. Liu, Z. G. Zeng, J. Wang, Multistability analysis of a general class of recurrent neural networks with non-monotonic activation functions and time-varying delays, Neural Netw., 79 (2016), 117–127.
  • View Article
  • Google Scholar


• [23] T. Liu, J. Zhao, D. J. Hill , Exponential synchronization of complex delayed dynamical networks with switching topology, IEEE Trans. Circuits Syst. I Reg. Papers, 57 (2010), 2967–2980
  • View Article
  • MathSciNet
  • Google Scholar


• [24] V. N. Phat, H. Trinh, Exponential stabilization of neural networks with various activation functions and mixed time-varying delays, IEEE Trans. Neural Netw., 21 (2010), 1180–1184.
  • View Article
  • Google Scholar


• [25] Y. Shen, J. Wang , Robustness analysis of global exponential stability of recurrent neural networks in the presence of time delays and random disturbances, IEEE Trans. Neural Netw., 23 (2012), 87–96.
  • View Article
  • Google Scholar


• [26] Z. S. Wang, S. B. Ding, Z. J. Huang, H. G. Zhang, Exponential stability and stabilization of delayed memristive neural networks based on quadratic convex combination method, IEEE Trans. Neural Netw. Learn. Syst., 27 (2016), 2337–2350.
  • View Article
  • Google Scholar


• [27] Z. S. Wang, L. Liu, Q. H. Shan, H. G. Zhang , Stability criteria for recurrent neural networks with time-varying delay based on secondary delay partitioning method, IEEE Trans. Neural Netw. Learn. Syst., 26 (2015), 2589–2595
  • View Article
  • MathSciNet
  • Google Scholar


• [28] Y.-W. Wang, W. Yang, J.-W. Xiao, Z.-G. Zeng, Impulsive multisynchronization of coupled multistable neural networks with time-varying delay, IEEE Trans. Neural Netw. Learn. Syst, 28 (2017), 1560–1571.
  • View Article
  • MathSciNet
  • Google Scholar


• [29] S. P.Wen, G. Bao, Z. G. Zeng, Y. R. Chen, T.W. Huang, Global exponential synchronization of memristor-based recurrent neural networks with time-varying delays, Neural Netw., 48 (2013), 195–203.
  • View Article
  • Google Scholar
  • MATH


• [30] S. P. Wen, Z. G. Zeng, Dynamics analysis of a class of memristor-based recurrent networks with time-varying delays in the presence of strong external stimuli, Neural Process. Lett., 35 (2012), 47–59.
  • View Article
  • Google Scholar


• [31] Z. G. Wu, P. Shi, H. Y. Su, J. Chu, Stochastic synchronization of Markovian jump neural networks with time-varying delay using sampled data, IEEE Trans. Cybern., 43 (2013), 1796–1806.
  • View Article
  • Google Scholar


• [32] A. L. Wu, Z. G. Zeng , Lagrange stability of memristive neural networks with discrete and distributed delays, IEEE Trans. Neural Netw. Learn. Syst., 25 (2014), 690–703.
  • View Article
  • Google Scholar


• [33] A. L. Wu, Z. G. Zeng, Output convergence of fuzzy neurodynamic system with piecewise constant argument of generalized type and time-varying input, IEEE Trans. Syst. Man Cybern. Syst., 46 (2016), 1689–1702.
  • View Article
  • Google Scholar


• [34] A. L. Wu, Z. G. Zeng, X. G. Song, Global MittagLeffler stabilization of fractional-order bidirectional associative memory neural networks, Neurocomputing, 177 (2016), 489–496.
  • View Article
  • Google Scholar


• [35] Z. G. Zeng, J. Wang, Global exponential stability of recurrent neural networks with time-varying delays in the presence of strong external stimuli , Neural Netw., 19 (2006), 1528–1537.
  • View Article
  • Google Scholar
  • MATH


• [36] W. B. Zhang, Y. Tang, Q. Y. Miao, W. Du, Exponential synchronization of coupled switched neural networks with modedependent impulsive effects, IEEE Trans. Neural Netw. Learn. Syst., 24 (2013), 1316–1326.
  • View Article
  • Google Scholar


• [37] W. B. Zhang, Y. Tang, Q. Y. Miao, J. A. Fang, Synchronization of stochastic dynamical networks under impulsive control with time delays, IEEE Trans. Neural Netw. Learn. Syst., 25 (2014), 1758–1768.
  • View Article
  • Google Scholar


• [38] H. G. Zhang, Z. S. Wang, D. R. Liu, A comprehensive review of stability analysis of continuous-time recurrent neural networks, IEEE Trans. Neural Netw. Learn. Syst., 25 (2014), 1229–1262.
  • View Article
  • Google Scholar


• [39] H. Zhao, L. X. Li, H. P. Peng, J. Kurths, J. H. Xiao, Y. X. Yang , Anti-synchronization for stochastic memristor-based neural networks with non-modeled dynamics via adaptive control approach, Eur. Phys. J. B, 88 (2015), 10 pages.
  • View Article
  • MathSciNet
  • Google Scholar


• [40] C. G. Zhou, X. Q. Zeng, J. J. Yu, H. B. Jiang, A unified associative memory model based on external inputs of continuous recurrent neural networks, Neurocomputing, 186 (2016), 44–53.
  • View Article
  • Google Scholar